Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/unit-test/lalg/sherman_morrison.cpp

Depends on

Code

#define UNITTEST
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include "../../../code/lalg/sherman_morrison.hpp"

#include "../../../code/lalg/mat.hpp"
#include "../../../code/lalg/ge_basic_mat.hpp"
#include "../../../code/lalg/inv_mat.hpp"
#include "../../../code/math/mint_2e61n1.hpp"
#include "../../../code/math/mint_d31.hpp"
#include "../../../code/math/mint_d63.hpp"
#include "../../../code/math/mint_ds.hpp"
#include "../../../code/math/mint_s30.hpp"
#include "../../../code/math/mint_s63.hpp"
#include "../../../code/math/mint_ss.hpp"
#include "../../../code/rand/gen.hpp"
#include "../base.hpp"

template <class mint>
void single_test(u32 n) {
  tifa_libs::rand::Gen<std::uniform_int_distribution<u32>> gen(1, std::numeric_limits<u32>::max());
  using mat = tifa_libs::math::matrix<mint>;
  auto is_0 = [](mint const& x) { return x.val() == 0; };
  auto ge = [&is_0](mat& m, bool f) { return tifa_libs::math::ge_basic(m, is_0, f); };

  mat L(n, n), U(n, n);
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j <= i; ++j) L(i, j) = gen();
  for (u32 i = 0; i < n; ++i)
    for (u32 j = i; j < n; ++j) U(i, j) = gen();

  mat I(n, n);
  for (u32 i = 0; i < n; ++i) I(i, i) = 1;

  mat A = L * U;
  mat inv_A = tifa_libs::math::inv_mat(A, is_0, ge).value();
  check(A * inv_A, I, check_param(L), check_param(U), check_param(A), check_param(inv_A));
  mat B = inv_A;
  vec<mint> u(n), v = A.data().back();
  for (u32 i = 0; i < n; ++i) u[i] = A(i, n - 1);
  tifa_libs::math::sherman_morrison(B, u, v);
  mat A2 = A + A.submat(0, n, n - 1, n) * A.submat(n - 1, n, 0, n);
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) {
      mint want = A(i, j) + u[i] * v[j];
      check(A2(i, j), want, check_param(A), check_param(u), check_param(v), check_param(A2));
    }
  check(B * A2, I, check_param(A), check_param(A2), check_param(B));
}

constexpr u32 MOD = 998244353;
constexpr u64 MOD64 = 3'799'912'185'593'857;

using mintd31 = tifa_libs::math::mint_d31<-1>;
using mintd63 = tifa_libs::math::mint_d63<-1>;
using mintds = tifa_libs::math::mint_ds<-1>;
using mints30 = tifa_libs::math::mint_s30<MOD>;
using mints63 = tifa_libs::math::mint_s63<MOD64>;
using mintss = tifa_libs::math::mint_ss<MOD>;

void test(u32 n) {
  single_test<tifa_libs::math::mint_2e61n1>(n);
  single_test<mintd31>(n);
  single_test<mintd63>(n);
  single_test<mintds>(n);
  single_test<mints30>(n);
  single_test<mints63>(n);
  single_test<mintss>(n);
}

int main() {
  auto tcase = tifa_libs::unittest::pre_test();

  mintd31::set_mod(MOD);
  mintd63::set_mod(MOD64);
  mintds::set_mod(MOD);

  switch (tcase) {
    case tifa_libs::unittest::ts_example_00: test(4); break;
    case tifa_libs::unittest::ts_example_01: test(10); break;
    case tifa_libs::unittest::ts_random_00: test(20); break;
    case tifa_libs::unittest::ts_random_01: test(30); break;
    case tifa_libs::unittest::ts_random_02: test(40); break;
    case tifa_libs::unittest::ts_random_03: break;
    case tifa_libs::unittest::ts_random_04: break;
    case tifa_libs::unittest::ts_random_05: break;
    case tifa_libs::unittest::ts_random_06: break;
    case tifa_libs::unittest::ts_random_07: break;
    case tifa_libs::unittest::ts_random_08: break;
    case tifa_libs::unittest::ts_random_09: break;
    default: break;
  }

  tifa_libs::unittest::post_test();
}
#line 1 "src/test_cpverifier/unit-test/lalg/sherman_morrison.cpp"
#define UNITTEST
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "src/code/lalg/sherman_morrison.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };


#line 5 "src/code/lalg/sherman_morrison.hpp"

namespace tifa_libs::math {

template <class Mat, class T = typename Mat::value_type>
requires std::same_as<T, typename Mat::value_type>
constexpr void sherman_morrison(Mat &inv_A, vec<T> const &u, vec<T> const &v) {
  u32 n = inv_A.row();
  assert(n == inv_A.col());
  vec<T> x(n), y(n);
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j)
      x[i] += inv_A(i, j) * u[j], y[j] += v[i] * inv_A(i, j);
  T sum = 1;
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) sum += v[i] * inv_A(i, j) * u[j];
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) inv_A(i, j) -= x[i] * y[j] / sum;
}

}  // namespace tifa_libs::math


#line 5 "src/test_cpverifier/unit-test/lalg/sherman_morrison.cpp"

#line 1 "src/code/lalg/mat.hpp"



#line 5 "src/code/lalg/mat.hpp"

namespace tifa_libs::math {

#define FOR1_(i, l, r) for (u32 i = (l), i##ed__ = (r); i < i##ed__; ++i)
#define FOR2_(i, row_l, row_r, j, col_l, col_r) \
  FOR1_ (i, row_l, row_r)                       \
    FOR1_ (j, col_l, col_r)

template <class T>
class matrix {
  vvec<T> d;

 public:
  using value_type = T;

  constexpr matrix(u32 row, u32 col, T const &v = T{}) : d(row, vec<T>(col, v)) { assert(row > 0 && col > 0); }
  explicit constexpr matrix(vvec<T> const &data) : d(data) { assert(data.size() > 0 && data[0].size() > 0); }

  constexpr u32 row() const { return (u32)d.size(); }
  constexpr u32 col() const { return (u32)d[0].size(); }
  constexpr vvec<T> const &data() const { return d; }
  constexpr vvec<T> &data() { return d; }
  constexpr typename vec<T>::reference operator()(u32 r, u32 c) { return d[r][c]; }
  constexpr typename vec<T>::const_reference operator()(u32 r, u32 c) const { return d[r][c]; }

  template <class F>
  constexpr void apply(F &&f) { apply_range(0, row(), 0, col(), std::forward<F>(f)); }
  template <class F>
  requires requires(F f, u32 i, u32 j, T &val) {
    f(i, j, val);
  }
  constexpr void apply_range(u32 row_l, u32 row_r, u32 col_l, u32 col_r, F &&f) {
    assert(row_l < row_r && row_r <= row());
    assert(col_l < col_r && col_r <= col());
    FOR2_ (i, row_l, row_r, j, col_l, col_r) f(i, j, (*this)(i, j));
  }

  friend std::istream &operator>>(std::istream &is, matrix &mat) {
    u32 r_ = mat.row(), c_ = mat.col();
    FOR2_ (i, 0, r_, j, 0, c_) is >> mat(i, j);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, matrix const &mat) {
    u32 r_ = mat.row(), c_ = mat.col();
    FOR2_ (i, 0, r_ - 1, j, 0, c_) os << mat(i, j) << " \n"[j + 1 == c_];
    os << mat(r_ - 1, 0);
    FOR1_ (j, 1, c_) os << ' ' << mat(r_ - 1, j);
    return os;
  }

  constexpr matrix submat(u32 row_l, u32 row_r, u32 col_l, u32 col_r) const {
    assert(row_l < row_r && row_r <= row());
    assert(col_l < col_r && col_r <= col());
    matrix ret(row_r - row_l, col_r - col_l);
    ret.apply_range(0, ret.row(), 0, ret.col(), [this, row_l, col_l](u32 i, u32 j, T &v) { v = (*this)(i + row_l, j + col_l); });
    return ret;
  }

  constexpr void swap_row(u32 r1, u32 r2) {
    assert(r1 < row() && r2 < row());
    if (r1 == r2) return;
    std::swap(d[r1], d[r2]);
  }
  constexpr void swap_col(u32 c1, u32 c2) {
    assert(c1 < col() && c2 < col());
    if (c1 == c2) return;
    FOR1_ (i, 0, row()) std::swap((*this)(i, c1), (*this)(i, c2));
  }

  constexpr matrix operator-() const {
    if constexpr (std::is_same_v<T, bool>) return *this;
    else {
      matrix ret = *this;
      ret.apply_range(0, row(), 0, col(), [](u32, u32, T &v) { v = -v; });
      return ret;
    }
  }

  friend constexpr matrix operator+(matrix l, T const &v) { return l += v; }
  friend constexpr matrix operator+(T const &v, matrix l) { return l += v; }
  constexpr matrix &operator+=(T const &v) {
    if constexpr (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&v](u32, u32, auto &val) { val = val ^ v; });
    else apply_range(0, row(), 0, col(), [&v](u32, u32, T &val) { val += v; });
    return *this;
  }
  friend constexpr matrix operator-(matrix l, T const &v) { return l -= v; }
  constexpr matrix &operator-=(T const &v) {
    if constexpr (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&v](u32, u32, auto &val) { val = val ^ v; });
    else apply_range(0, row(), 0, col(), [&v](u32, u32, T &val) { val -= v; });
    return *this;
  }
  friend constexpr matrix operator*(matrix l, T const &v) { return l *= v; }
  friend constexpr matrix operator*(T const &v, matrix l) { return l *= v; }
  constexpr matrix &operator*=(T const &v) {
    if constexpr (std::is_same_v<T, bool>) {
      if (!v)
        for (auto &i : d) i.clear(), i.resize(col());
      return *this;
    } else apply_range(0, row(), 0, col(), [&v](u32, u32, T &val) { val *= v; });
    return *this;
  }

  friend constexpr matrix operator+(matrix l, matrix const &r) { return l += r; }
  constexpr matrix &operator+=(matrix const &r) {
    assert(row() == r.row() && col() == r.col());
    if constexpr (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, auto &val) { val = val ^ r(i, j); });
    else apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, T &val) { val += r(i, j); });
    return *this;
  }
  friend constexpr matrix operator-(matrix l, matrix const &r) { return l -= r; }
  constexpr matrix &operator-=(matrix const &r) {
    assert(row() == r.row() && col() == r.col());
    if constexpr (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, auto &val) { val = val ^ r(i, j); });
    else apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, T &val) { val -= r(i, j); });
    return *this;
  }

  friend constexpr matrix operator*(matrix const &l, matrix const &r) {
    u32 i_ = l.row(), j_ = l.col(), k_ = r.col();
    assert(j_ == r.row());
    matrix ret(i_, k_);
    FOR1_ (i, 0, i_)
      FOR1_ (j, 0, j_)
        FOR1_ (k, 0, k_)
          if constexpr (std::is_same_v<T, bool>) ret(i, k) = ret(i, k) ^ (l(i, j) && r(j, k));
          else ret(i, k) += l(i, j) * r(j, k);
    return ret;
  }
  constexpr matrix &operator*=(matrix const &r) { return *this = *this * r; }

  constexpr vec<T> lproj(vec<T> const &x) const {
    u32 r_ = row(), c_ = col();
    assert(r_ == x.size());
    vec<T> ret(c_);
    for (u32 i = 0; i < c_; ++i)
      if constexpr (std::is_same_v<T, bool>) ret[i] = std::transform_reduce(d[i].begin(), d[i].end(), x.begin(), false, std::bit_xor<bool>{}, std::bit_and<bool>{});
      else ret[i] = std::transform_reduce(d[i].begin(), d[i].end(), x.begin(), T{});
    return ret;
  }

  constexpr bool operator==(matrix const &r) const {
    if (row() != r.row() || col() != r.col()) return 0;
    FOR1_ (i, 0, row())
      if (d[i] != r.d[i]) return 0;
    return 1;
  }
};

#undef FOR1_
#undef FOR2_

}  // namespace tifa_libs::math


#line 1 "src/code/lalg/ge_basic_mat.hpp"



#line 1 "src/code/lalg/ge_swapr_mat_.hpp"



#line 5 "src/code/lalg/ge_swapr_mat_.hpp"

namespace tifa_libs::math::ge_impl_ {

template <class Mat>
constexpr bool swapr__(Mat &mat, u32 &r_, u32 r_pre_, u32 r_end) {
  r_ = r_pre_;
  for (u32 j = r_ + 1; j < r_end; ++j)
    if (mat.data()[r_] < mat.data()[j]) r_ = j;
  if (r_ != r_pre_) {
    mat.swap_row(r_, r_pre_);
    return true;
  }
  return false;
}

}  // namespace tifa_libs::math::ge_impl_


#line 5 "src/code/lalg/ge_basic_mat.hpp"

namespace tifa_libs::math {

template <class Mat, class Is0>
requires requires(Is0 is0, typename Mat::value_type t) {
  { is0(t) } -> std::same_as<bool>;
}
constexpr i32 ge_basic(Mat& mat, Is0&& is0, bool clear_u = true) {
  using T = typename Mat::value_type;
  u32 r_ = mat.row(), c_ = mat.col(), rk_max = std::min(r_, c_);
  u32 rk = 0;
  bool neg = false;
  for (u32 i = 0, now_row = 0, j_ = i; i < mat.row(); ++i) {
    neg ^= ge_impl_::swapr__(mat, now_row, rk, mat.row());
    j_ = std::max(j_, i);
    while (j_ < c_ && is0(mat(rk, j_))) ++j_;
    if (j_ == c_) break;
    for (u32 j = clear_u ? 0 : rk + 1; j < mat.row(); ++j) {
      if (j == rk || is0(mat(j, j_))) continue;
      T _ = mat(j, j_) / mat(rk, j_);
      mat(j, j_) = 0;
      for (u32 k = j_ + 1; k < c_; ++k) mat(j, k) -= mat(rk, k) * _;
    }
    if (++rk >= rk_max) break;
  }
  return neg ? -((i32)rk) : (i32)rk;
}

}  // namespace tifa_libs::math


#line 1 "src/code/lalg/inv_mat.hpp"



#line 1 "src/code/lalg/merge_lr_mat.hpp"



#line 5 "src/code/lalg/merge_lr_mat.hpp"

namespace tifa_libs::math {

// [l] [r] -> [l r]
template <class T>
constexpr matrix<T> merge_lr_mat(matrix<T> const &l, matrix<T> const &r) {
  u32 r_ = l.row();
  assert(r_ == r.row());
  u32 lc_ = l.col(), rc_ = r.col(), c_ = lc_ + rc_;
  matrix<T> ret(r_, c_);
  ret.apply_range(0, r_, 0, lc_, [&l](u32 i, u32 j, T &val) { val = l(i, j); });
  ret.apply_range(0, r_, lc_, c_, [lc_, &r](u32 i, u32 j, T &val) { val = r(i, j - lc_); });
  return ret;
}

}  // namespace tifa_libs::math


#line 5 "src/code/lalg/inv_mat.hpp"

namespace tifa_libs::math {

template <class T, class Is0, class Ge>
requires requires(Is0 is0, Ge ge, T t, matrix<T> A, bool clear_u) {
  { is0(t) } -> std::same_as<bool>;
  { ge(A, clear_u) } -> std::same_as<i32>;
}
constexpr std::optional<matrix<T>> inv_mat(matrix<T> const& mat, Is0&& is0, Ge&& ge) {
  u32 n = mat.row();
  if (n != mat.col()) return {};
  matrix<T> ret(n, n);
  for (u32 i = 0; i < n; ++i) ret(i, i) = 1;
  if ((u64)abs(ge(ret = merge_lr_mat(mat, ret), true)) != n) return {};
  for (u32 i = 0; i < n; ++i)
    if (is0(ret(i, i))) return {};
  ret.apply_range(0, n, n, n * 2, [&ret](u32 i, u32, T& val) { val /= ret(i, i); });
  return ret.submat(0, n, n, n * 2);
}

}  // namespace tifa_libs::math


#line 1 "src/code/math/mint_2e61n1.hpp"



#line 1 "src/code/math/mint.hpp"



#line 1 "src/code/nt/inverse.hpp"



#line 1 "src/code/nt/inv_gcd.hpp"



#line 1 "src/code/math/safe_mod.hpp"



#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 5 "src/code/math/safe_mod.hpp"

namespace tifa_libs::math {

template <sint_c T>
constexpr T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }

}  // namespace tifa_libs::math


#line 1 "src/code/nt/exgcd.hpp"



#line 5 "src/code/nt/exgcd.hpp"

namespace tifa_libs::math {

// Binary exgcd
template <uint_c U, bool only_x = false>
constexpr auto exgcd_b(U a, U b) {
  using T = to_sint_t<U>;
  if constexpr (only_x) {
    if (!a) return std::make_tuple(b, (T)0);
    if (!b) return std::make_tuple(a, (T)1);
  } else {
    if (!a) return std::make_tuple(b, (T)0, (T) !!b);
    if (!b) return std::make_tuple(a, (T)1, (T)0);
  }
  auto r = std::__countr_zero(a | b);
  a >>= r, b >>= r;
  T x = (T)a, y = (T)b;
  T s = 1, t = 0, u = 0, v = 1;
  while (x) {
    while (!(x & 1)) {
      x /= 2;
      if (!((s | t) & 1)) s /= 2, t /= 2;
      else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
    }
    while (!(y & 1)) {
      y /= 2;
      if (!((u | v) & 1)) u /= 2, v /= 2;
      else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
    }
    if (x >= y) x -= y, s -= u, t -= v;
    else y -= x, u -= s, v -= t;
  }
  if (y > 1) a /= (U)y, b /= (U)y;
  if (a && (U)abs(v) >= a) {
    T _ = v / (T)a;
    v -= _ * (T)a, u += _ * (T)b;
  }
  if (b && (U)abs(u) >= b) {
    T _ = u / (T)b;
    u -= _ * (T)b, v += _ * (T)a;
  }
  if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if (T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if constexpr (only_x) return std::make_tuple(U(y << r), u);
  else return std::make_tuple(U(y << r), u, v);
}
// @return then return tuple(g, x[, y]) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T, bool only_x = false>
constexpr auto exgcd(T a, T b) {
  using U = to_uint_t<T>;
  if (auto [x, y] = std::minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
  if constexpr (only_x) {
    T s = 1, u = 0;
    while (b) {
      T c = a / b;
      std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s);
  } else {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
      T c = a / b;
      std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s, t);
  }
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/inv_gcd.hpp"

namespace tifa_libs::math {

template <uint_c T>
constexpr ptt<T> inv_gcd(T n, T mod) {
  using U = to_sint_t<T>;
  auto [g, x] = exgcd<U, true>(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/inverse.hpp"

namespace tifa_libs::math {

template <uint_c T, uint_c U>
constexpr U inverse(T n, U mod) {
  auto [g, x] = inv_gcd(U(n % mod), mod);
  assert(g == 1);
  return x;
}

}  // namespace tifa_libs::math


#line 6 "src/code/math/mint.hpp"

namespace tifa_libs::math {

template <class D, uint_c Rt>
class mint {
  constexpr D const &d() const { return static_cast<D const &>(*this); }
  constexpr D &d() { return static_cast<D &>(*this); }

 protected:
  Rt v_{};

 public:
  constexpr mint() {}
  template <int_c T>
  constexpr mint(T v) : v_(D::mod_(v)) {}
  constexpr operator D() { return d(); }

  using raw_type = Rt;
  using sraw_type = to_sint_t<Rt>;
  static constexpr raw_type mod() { return D::mod_(); }
  static constexpr sraw_type smod() { return (sraw_type)D::mod_(); }
  constexpr raw_type val() const { return d().val_(); }
  constexpr sraw_type sval() const { return (sraw_type)d().val_(); }
  constexpr raw_type &data() { return d().data_(); }

  template <int_c T>
  explicit constexpr operator T() const { return (T)val(); }
  constexpr mint &operator+=(mint const &r) { return d().adde_(r.d()); }
  constexpr mint &operator-=(mint const &r) { return d().sube_(r.d()); }
  constexpr mint &operator*=(mint const &r) { return d().mule_(r.d()); }
  constexpr mint &operator/=(mint const &r) { return *this = *this * r.inv(); }
  constexpr mint const &operator+() const { return *this; }
  constexpr mint operator-() const { return d().neg_(); }
  constexpr mint inv() const { return inverse(val(), mod()); }
  friend constexpr mint operator+(mint l, mint const &r) { return l += r; }
  friend constexpr mint operator-(mint l, mint const &r) { return l -= r; }
  friend constexpr mint operator*(mint l, mint const &r) { return l *= r; }
  friend constexpr mint operator/(mint l, mint const &r) { return l /= r; }
  friend constexpr bool operator==(mint const &l, mint const &r) { return l.val() == r.val(); }
  friend constexpr auto operator<=>(mint const &l, mint const &r) { return l.sval() - r.sval(); }
  friend std::istream &operator>>(std::istream &is, mint &x) {
    i64 _;
    is >> _;
    x = mint(_);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, mint const &x) { return os << x.val(); }
  friend constexpr mint abs(mint const &x) { return x.val(); }
};

}  // namespace tifa_libs::math


#line 5 "src/code/math/mint_2e61n1.hpp"

namespace tifa_libs::math {

class mint_2e61n1 : public mint<mint_2e61n1, u64> {
  using base = mint<mint_2e61n1, u64>;
  friend base;

  static constexpr u64 MOD = (1ull << 61) - 1;
  static constexpr u64 _30 = (1 << 30) - 1, _31 = (1u << 31) - 1;

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_2e61n1() {}
  template <int_c T>
  constexpr mint_2e61n1(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  // clang-format off
  template <uint_c T>
  static constexpr raw_t mod_(T x) { return x < MOD ? (raw_t)x : (x = T(((raw_t)x & MOD) + ((raw_t)x >> 61))) >= MOD ? x - MOD : (raw_t)x; }
  template <sint_c T>
  static constexpr raw_t mod_(T x) { return x >= 0 ? mod_(to_uint_t<T>(x)) : MOD - mod_(to_uint_t<T>(-x)); }
  // clang-format on
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const { return this->v_; }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_2e61n1 neg_() const { return mint_2e61n1(MOD - val_()); }
  constexpr mint_2e61n1 &adde_(mint_2e61n1 const &r) {
    data_() = mod_(val_() + r.val_());
    return *this;
  }
  constexpr mint_2e61n1 &sube_(mint_2e61n1 const &r) {
    val_() < r.val_() ? data_() = mod_(val_() + MOD - r.val_()) : data_() -= r.val_();
    return *this;
  }
  constexpr mint_2e61n1 &mule_(mint_2e61n1 const &r) {
    raw_t au = val_() >> 31, ad = val_() & _31, bu = r.val_() >> 31, bd = r.val_() & _31, _ = ad * bu + au * bd;
    data_() = mod_(((au * bu) << 1) + ad * bd + ((_ & _30) << 31) + (_ >> 30));
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/math/mint_d31.hpp"



#line 5 "src/code/math/mint_d31.hpp"

namespace tifa_libs::math {

template <int ID>
class mint_d31 : public mint<mint_d31<ID>, u32> {
  using base = mint<mint_d31<ID>, u32>;
  friend base;

  static inline u32 R, R2, MOD, MOD_ODD, OFFSET, MASK;

  static constexpr u32 norm(i32 x) { return u32(x + (-(x < 0) & (i32)MOD)); }
  static constexpr u32 redc(u64 x) {
    u32 t = u32((x + u64((u32)x * R) * MOD_ODD) >> 32);
    return t - (MOD_ODD & -((MOD_ODD - 1 - t) >> 31));
  }
  static constexpr u32 tsf(u32 x) { return redc(u64(x % MOD_ODD) * R2) << OFFSET | (x & MASK); }

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u32 m) {
    assert(!(m == 1 || m >> 31));
    for (MOD = MOD_ODD = m, OFFSET = 0; (MOD_ODD & 1) == 0; ++OFFSET, MOD_ODD /= 2);
    MASK = (1 << OFFSET) - 1;
    u32 t = 2, iv = MOD_ODD * (t - MOD_ODD * MOD_ODD);
    iv *= t - MOD_ODD * iv, iv *= t - MOD_ODD * iv;
    R = iv * (MOD_ODD * iv - t);
    R2 = u32(-u64(MOD_ODD) % MOD_ODD);
  }

  constexpr mint_d31() {}
  template <int_c T>
  constexpr mint_d31(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <int_c T>
  static constexpr raw_t mod_(T v) { return tsf(norm(i32(v % (std::conditional_t<sint_c<T>, i32, u32>)mod_()))); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t h = redc(this->v_ >> OFFSET);
    return ((h - this->v_) * R & MASK) * MOD_ODD + h;
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_d31 neg_() const {
    mint_d31 res;
    raw_t h = this->v_ >> OFFSET;
    res.v_ = (((MOD_ODD & -(h != 0)) - h) << OFFSET) | (-this->v_ & MASK);
    return res;
  }
  constexpr mint_d31 &adde_(mint_d31 const &r) {
    raw_t h = (this->v_ >> OFFSET) + (r.v_ >> OFFSET) - MOD_ODD;
    this->v_ = ((h + (MOD_ODD & -(h >> 31))) << OFFSET) | ((this->v_ + r.v_) & MASK);
    return *this;
  }
  constexpr mint_d31 &sube_(mint_d31 const &r) {
    raw_t h = (this->v_ >> OFFSET) - (r.v_ >> OFFSET);
    this->v_ = ((h + (MOD_ODD & -(h >> 31))) << OFFSET) | ((this->v_ - r.v_) & MASK);
    return *this;
  }
  constexpr mint_d31 &mule_(mint_d31 const &r) {
    this->v_ = (redc((u64)(this->v_ >> OFFSET) * (r.v_ >> OFFSET)) << OFFSET) | ((this->v_ * r.v_) & MASK);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/math/mint_d63.hpp"



#line 5 "src/code/math/mint_d63.hpp"

namespace tifa_libs::math {

template <int ID>
class mint_d63 : public mint<mint_d63<ID>, u64> {
  using base = mint<mint_d63<ID>, u64>;
  friend base;

  static inline u64 MOD, R, R2;

  static constexpr u64 mul_h(u64 x, u64 y) {
    u64 a = x >> 32, b = (u32)x, c = y >> 32, d = (u32)y, ad = a * d, bc = b * c;
    return a * c + (ad >> 32) + (bc >> 32) + (((ad & 0xFFFFFFFF) + (bc & 0xFFFFFFFF) + (b * d >> 32)) >> 32);
  }
  static constexpr u64 redc_mul(u64 x, u64 y) {
    u64 res = mul_h(x, y) - mul_h(x * y * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  static constexpr u64 norm(i64 x) { return u64(x + i64(MOD & u64(-(x < 0)))); }

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u64 m) {
    assert(!((m & 1) == 0 || m == 1 || m >> 63));
    MOD = m;
    u64 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv, iv *= t - MOD * iv;
    R = iv * (t - MOD * iv);
    R2 = -MOD % MOD;
    for (u32 i = 0; i != 64; ++i)
      if ((R2 *= 2) >= MOD) R2 -= MOD;
  }

  constexpr mint_d63() {}
  template <int_c T>
  constexpr mint_d63(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <int_c T>
  static constexpr raw_t mod_(T v) { return redc_mul(norm(i64(v % (std::conditional_t<sint_c<T>, i64, u64>)mod_())), R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t res = -mul_h(this->v_ * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_d63 neg_() const {
    mint_d63 res;
    res.v_ = (MOD & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_d63 &adde_(mint_d63 const &r) {
    this->v_ += r.v_ - MOD, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &sube_(mint_d63 const &r) {
    this->v_ -= r.v_, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &mule_(mint_d63 const &r) {
    this->v_ = redc_mul(this->v_, r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/math/mint_ds.hpp"



#line 5 "src/code/math/mint_ds.hpp"

namespace tifa_libs::math {

template <i32 ID>
class mint_ds : public mint<mint_ds<ID>, u32> {
  using base = mint<mint_ds<ID>, u32>;
  friend base;

  struct barrett {
    u32 m_;
    u64 im;
    // @param m `1 <= m < 2^31`
    explicit constexpr barrett(u32 m = 998244353) : m_(m), im(-1_u64 / m + 1) {}
    // @return m
    constexpr u32 umod() const { return m_; }
    constexpr u32 mul(u32 a, u32 b) const {
      u64 z = (u64)a * b, x = (u64)(((u128)z * im) >> 64);
      u32 v = (u32)(z - x * m_);
      return v + (m_ <= v ? m_ : 0);
    }
  };

  static inline barrett bt_;

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u32 m) {
    assert(1 <= m);
    bt_ = barrett(m);
  }

  constexpr mint_ds() {}
  template <int_c T>
  constexpr mint_ds(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <sint_c T>
  static constexpr raw_t mod_(T v) {
    i64 x = i64(v % (i64)mod_());
    return raw_t(x + (x < 0 ? mod_() : 0));
  }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return raw_t(v % mod_()); }
  static constexpr raw_t mod_() { return bt_.umod(); }
  constexpr raw_t val_() const { return this->v_; }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_ds neg_() const { return -(sraw_t)val_(); }
  constexpr mint_ds &adde_(mint_ds const &r) {
    data_() += r.val_();
    if (val_() >= mod_()) data_() -= mod_();
    return *this;
  }
  constexpr mint_ds &sube_(mint_ds const &r) {
    data_() -= r.val_();
    if (val_() >= mod_()) data_() += mod_();
    return *this;
  }
  constexpr mint_ds &mule_(mint_ds const &r) {
    data_() = bt_.mul(val_(), r.val_());
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/math/mint_s30.hpp"



#line 5 "src/code/math/mint_s30.hpp"

namespace tifa_libs::math {

template <u32 MOD>
class mint_s30 : public mint<mint_s30<MOD>, u32> {
  using base = mint<mint_s30<MOD>, u32>;
  friend base;

  static constexpr u32 MOD2 = MOD << 1;
  static constexpr u32 R = []() {
    u32 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv;
    return iv * (MOD * iv - t);
  }();
  static constexpr u32 R2 = -(u64)(MOD) % MOD;

  static_assert(MOD & 1);
  static_assert(-R * MOD == 1);
  static_assert((MOD >> 30) == 0);
  static_assert(MOD != 1);

  static constexpr u32 reduce(u64 x) { return u32((x + u64((u32)x * R) * MOD) >> 32); }
  static constexpr u32 norm(u32 x) { return x - (MOD & -((MOD - 1 - x) >> 31)); }

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_s30() {}
  template <int_c T>
  constexpr mint_s30(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <sint_c T>
  static constexpr raw_t mod_(T v) { return reduce(u64(v % (i32)mod_() + (i32)mod_()) * R2); }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return reduce(u64(v % mod_()) * R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const { return norm(reduce(this->v_)); }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_s30 neg_() const {
    mint_s30 res;
    res.v_ = (MOD2 & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_s30 &adde_(mint_s30 const &r) {
    this->v_ += r.v_ - MOD2, this->v_ += MOD2 & -(this->v_ >> 31);
    return *this;
  }
  constexpr mint_s30 &sube_(mint_s30 const &r) {
    this->v_ -= r.v_, this->v_ += MOD2 & -(this->v_ >> 31);
    return *this;
  }
  constexpr mint_s30 &mule_(mint_s30 const &r) {
    this->v_ = reduce(u64(this->v_) * r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/math/mint_s63.hpp"



#line 5 "src/code/math/mint_s63.hpp"

namespace tifa_libs::math {

template <u64 MOD>
class mint_s63 : public mint<mint_s63<MOD>, u64> {
  using base = mint<mint_s63<MOD>, u64>;
  friend base;

  static constexpr u64 R = []() {
    u64 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv, iv *= t - MOD * iv;
    return iv * (t - MOD * iv);
  }();
  static constexpr u64 R2 = []() {
    u64 iv = -MOD % MOD;
    for (u32 i = 0; i != 64; ++i)
      if ((iv *= 2) >= MOD) iv -= MOD;
    return iv;
  }();

  static_assert(MOD & 1);
  static_assert(R * MOD == 1);
  static_assert((MOD >> 63) == 0);
  static_assert(MOD != 1);

  static constexpr u64 mulh(u64 x, u64 y) {
    u64 a = x >> 32, b = (u32)(x), c = y >> 32, d = (u32)(y), ad = a * d, bc = b * c;
    return a * c + (ad >> 32) + (bc >> 32) + (((ad & 0xFFFFFFFF) + (bc & 0xFFFFFFFF) + (b * d >> 32)) >> 32);
  }
  static constexpr u64 redc_mul(u64 x, u64 y) {
    u64 res = mulh(x, y) - mulh(x * y * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  static constexpr u64 norm(i64 x) { return (u64)x + (MOD & -(x < 0)); }

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_s63() {}
  template <int_c T>
  constexpr mint_s63(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <int_c T>
  static constexpr raw_t mod_(T v) { return redc_mul(norm(v % (std::conditional_t<sint_c<T>, i64, u64>)mod_()), R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t res = -mulh(this->v_ * R, mod_());
    return res + (MOD & -(res >> 63));
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_s63 neg_() const {
    mint_s63 res;
    res.v_ = (MOD & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_s63 &adde_(mint_s63 const &r) {
    this->v_ += r.v_ - MOD, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_s63 &sube_(mint_s63 const &r) {
    this->v_ -= r.v_, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_s63 &mule_(mint_s63 const &r) {
    this->v_ = redc_mul(this->v_, r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/math/mint_ss.hpp"



#line 5 "src/code/math/mint_ss.hpp"

namespace tifa_libs::math {

template <u32 MOD>
class mint_ss : public mint<mint_ss<MOD>, u32> {
  using base = mint<mint_ss<MOD>, u32>;
  friend base;
  static_assert(MOD >= 1);

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_ss() {}
  template <int_c T>
  constexpr mint_ss(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <sint_c T>
  static constexpr raw_t mod_(T v) {
    i64 x = i64(v % (i64)mod_());
    return raw_t(x + (x < 0 ? mod_() : 0));
  }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return raw_t(v % mod_()); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const { return this->v_; }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_ss neg_() const { return -(sraw_t)val_(); }
  constexpr mint_ss &adde_(mint_ss const &r) {
    data_() += r.val_();
    if (val_() >= mod_()) data_() -= mod_();
    return *this;
  }
  constexpr mint_ss &sube_(mint_ss const &r) {
    data_() -= r.val_();
    if (val_() >= mod_()) data_() += mod_();
    return *this;
  }
  constexpr mint_ss &mule_(mint_ss const &r) {
    data_() = u32((u64)val_() * r.val_() % mod_());
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/rand/gen.hpp"



#line 5 "src/code/rand/gen.hpp"

namespace tifa_libs::rand {

template <class Distri>
class Gen {
  std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::mt19937, std::mt19937_64> re;
  Distri dist;

 public:
  using random_engine = decltype(re);
  using distribution = Distri;
  using result_type = typename Distri::result_type;

  constexpr Gen() : re(std::random_device{}()), dist() {}
  constexpr Gen(result_type a, result_type b) : re(std::random_device{}()), dist(a, b) {}

  constexpr void set_range(result_type a, result_type b) { dist = Distri(a, b); }
  constexpr random_engine& rand_eng() { return re; }
  constexpr Distri& distrib() { return dist; }

  void reset_seed() { re.seed((result_type)std::chrono::duration_cast<std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::chrono::seconds, std::chrono::nanoseconds>>(std::chrono::high_resolution_clock::now().time_since_epoch()).count()); }
  constexpr result_type operator()() { return dist(re); }
  result_type next() { return dist(re); }
};

}  // namespace tifa_libs::rand


#line 1 "src/test_cpverifier/unit-test/base.hpp"



#line 1 "src/code/io/ios128.hpp"



#line 5 "src/code/io/ios128.hpp"

inline std::istream &operator>>(std::istream &is, i128 &n) {
  bool neg = false;
  while (!neg && !isdigit(is.peek())) {
    if (is.peek() == '-') neg = true;
    is.get();
  }
  n = 0;
  while (isdigit(is.peek())) (n *= 10) += is.get() & 15;
  if (neg) n = -n;
  return is;
}
inline std::istream &operator>>(std::istream &is, u128 &n) {
  while (!isdigit(is.peek())) is.get();
  n = 0;
  while (isdigit(is.peek())) (n *= 10) += is.get() & 15;
  return is;
}
inline std::ostream &operator<<(std::ostream &os, u128 n) {
  if (n > 9) os << n / 10;
  os << (uint_fast32_t)(n % 10);
  return os;
}
inline std::ostream &operator<<(std::ostream &os, i128 n) {
  if (n < 0) {
    os << '-';
    n = -n;
  }
  return os << (u128)n;
}


#line 1 "src/code/io/ios_container.hpp"



#line 5 "src/code/io/ios_container.hpp"

template <tifa_libs::container_c T>
std::istream &operator>>(std::istream &is, T &x) {
  for (auto &i : x) is >> i;
  return is;
}
template <tifa_libs::container_c T>
std::ostream &operator<<(std::ostream &os, T const &x) {
  if (x.begin() == x.end()) return os;
  auto it = x.begin();
  os << *it++;
  for (; it != x.end(); ++it) os << ' ' << *it;
  return os;
}


#line 1 "src/code/io/ios_pair.hpp"



#line 5 "src/code/io/ios_pair.hpp"

template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) { return is >> p.first >> p.second; }
template <class T, class U>
std::ostream &operator<<(std::ostream &os, std::pair<T, U> const &p) { return os << p.first << ' ' << p.second; }


#line 1 "src/code/io/ios_tuple.hpp"



#line 5 "src/code/io/ios_tuple.hpp"

template <class... Ts>
std::istream &operator>>(std::istream &is, std::tuple<Ts...> &p) {
  std::apply([&](Ts &...targs) { ((is >> targs), ...); }, p);
  return is;
}
template <class... Ts>
std::ostream &operator<<(std::ostream &os, std::tuple<Ts...> const &p) {
  std::apply(
      [&](Ts const &...targs) {
        usz n = 0;
        ((os << targs << (++n != sizeof...(Ts) ? " " : "")), ...);
      },
      p);
  return os;
}


#line 10 "src/test_cpverifier/unit-test/base.hpp"

namespace tifa_libs::unittest {

namespace detail__ {

template <class T>
strn to_str(T const &x) {
  std::stringstream ss;
  ss << std::fixed << std::setprecision(12) << x;
  return ss.str();
}

template <class T, class... Ts>
void check_(strn const &pretty_func, strn const &got_str, T const &got, strn const &want_str, T const &want, Ts... param) {
  if constexpr (sizeof...(param) == 0) {
    if (got != want) throw std::runtime_error(pretty_func + ": got \"" + got_str + "\" = " + to_str(got) + ", want \"" + want_str + "\" = " + to_str(want));
  } else {
    if (got != want) throw std::runtime_error(pretty_func + ": got \"" + got_str + "\" = " + to_str(got) + ", want \"" + want_str + "\" = " + to_str(want) + " with" + ((" " + param.first + " = " + ::tifa_libs::unittest::detail__::to_str(param.second) + " ;") + ...));
  }
}

template <class... Ts>
void check_bool_(strn const &pretty_func, strn const &expression, bool res, Ts... param) {
  if constexpr (sizeof...(param) == 0) {
    if (!res) throw std::runtime_error(pretty_func + " :\"" + expression + "\" failed");
  } else {
    if (!res) throw std::runtime_error(pretty_func + " :\"" + expression + "\" failed with" + ((" " + param.first + " = " + ::tifa_libs::unittest::detail__::to_str(param.second) + " ;") + ...));
  }
}

}  // namespace detail__

enum TESTCASE { ts_local,
                ts_example_00,
                ts_example_01,
                ts_random_00,
                ts_random_01,
                ts_random_02,
                ts_random_03,
                ts_random_04,
                ts_random_05,
                ts_random_06,
                ts_random_07,
                ts_random_08,
                ts_random_09 };

inline const std::map<ptt<u32>, TESTCASE> testcase_id{
    {{1234, 5678}, ts_example_00},
    {{1000000000, 1000000000}, ts_example_01},
    {{192279220, 156648746}, ts_random_00},
    {{264704197, 120999146}, ts_random_01},
    {{682152023, 451794314}, ts_random_02},
    {{627477696, 504915182}, ts_random_03},
    {{729561619, 415335212}, ts_random_04},
    {{173330281, 220603612}, ts_random_05},
    {{841413509, 58432763}, ts_random_06},
    {{251229786, 256388306}, ts_random_07},
    {{118232767, 222490630}, ts_random_08},
    {{907649120, 290651129}, ts_random_09}};

inline void post_test([[maybe_unused]] ptt<u32> const &p = {0, 0}) {
#ifndef LOCAL_
  static ptt<u32> p_{0, 0};
  if (p.first || p.second) {
    p_ = p;
    return;
  }
  std::cout << p_.first + p_.second << '\n';
  exit(0);
#endif
}

inline TESTCASE pre_test() {
#ifndef LOCAL_
  ptt<u32> p;
  std::cin >> p.first >> p.second;
  post_test(p);
  return testcase_id.at(p);
#else
  return ts_local;
#endif
}

#define check(got, want, ...) ::tifa_libs::unittest::detail__::check_(__PRETTY_FUNCTION__, #got, got, #want, want __VA_OPT__(, ) __VA_ARGS__)
#define check_bool(expression, ...) ::tifa_libs::unittest::detail__::check_bool_(__PRETTY_FUNCTION__, #expression, expression __VA_OPT__(, ) __VA_ARGS__)
#define check_param(x) \
  std::pair<std::string, decltype(x)> { #x " = ", x }

}  // namespace tifa_libs::unittest


#line 18 "src/test_cpverifier/unit-test/lalg/sherman_morrison.cpp"

template <class mint>
void single_test(u32 n) {
  tifa_libs::rand::Gen<std::uniform_int_distribution<u32>> gen(1, std::numeric_limits<u32>::max());
  using mat = tifa_libs::math::matrix<mint>;
  auto is_0 = [](mint const& x) { return x.val() == 0; };
  auto ge = [&is_0](mat& m, bool f) { return tifa_libs::math::ge_basic(m, is_0, f); };

  mat L(n, n), U(n, n);
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j <= i; ++j) L(i, j) = gen();
  for (u32 i = 0; i < n; ++i)
    for (u32 j = i; j < n; ++j) U(i, j) = gen();

  mat I(n, n);
  for (u32 i = 0; i < n; ++i) I(i, i) = 1;

  mat A = L * U;
  mat inv_A = tifa_libs::math::inv_mat(A, is_0, ge).value();
  check(A * inv_A, I, check_param(L), check_param(U), check_param(A), check_param(inv_A));
  mat B = inv_A;
  vec<mint> u(n), v = A.data().back();
  for (u32 i = 0; i < n; ++i) u[i] = A(i, n - 1);
  tifa_libs::math::sherman_morrison(B, u, v);
  mat A2 = A + A.submat(0, n, n - 1, n) * A.submat(n - 1, n, 0, n);
  for (u32 i = 0; i < n; ++i)
    for (u32 j = 0; j < n; ++j) {
      mint want = A(i, j) + u[i] * v[j];
      check(A2(i, j), want, check_param(A), check_param(u), check_param(v), check_param(A2));
    }
  check(B * A2, I, check_param(A), check_param(A2), check_param(B));
}

constexpr u32 MOD = 998244353;
constexpr u64 MOD64 = 3'799'912'185'593'857;

using mintd31 = tifa_libs::math::mint_d31<-1>;
using mintd63 = tifa_libs::math::mint_d63<-1>;
using mintds = tifa_libs::math::mint_ds<-1>;
using mints30 = tifa_libs::math::mint_s30<MOD>;
using mints63 = tifa_libs::math::mint_s63<MOD64>;
using mintss = tifa_libs::math::mint_ss<MOD>;

void test(u32 n) {
  single_test<tifa_libs::math::mint_2e61n1>(n);
  single_test<mintd31>(n);
  single_test<mintd63>(n);
  single_test<mintds>(n);
  single_test<mints30>(n);
  single_test<mints63>(n);
  single_test<mintss>(n);
}

int main() {
  auto tcase = tifa_libs::unittest::pre_test();

  mintd31::set_mod(MOD);
  mintd63::set_mod(MOD64);
  mintds::set_mod(MOD);

  switch (tcase) {
    case tifa_libs::unittest::ts_example_00: test(4); break;
    case tifa_libs::unittest::ts_example_01: test(10); break;
    case tifa_libs::unittest::ts_random_00: test(20); break;
    case tifa_libs::unittest::ts_random_01: test(30); break;
    case tifa_libs::unittest::ts_random_02: test(40); break;
    case tifa_libs::unittest::ts_random_03: break;
    case tifa_libs::unittest::ts_random_04: break;
    case tifa_libs::unittest::ts_random_05: break;
    case tifa_libs::unittest::ts_random_06: break;
    case tifa_libs::unittest::ts_random_07: break;
    case tifa_libs::unittest::ts_random_08: break;
    case tifa_libs::unittest::ts_random_09: break;
    default: break;
  }

  tifa_libs::unittest::post_test();
}

Test cases

Env Name Status Elapsed Memory
g++-12 example_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 example_01 :heavy_check_mark: AC 8 ms 4 MB
g++-12 random_00 :heavy_check_mark: AC 14 ms 4 MB
g++-12 random_01 :heavy_check_mark: AC 28 ms 4 MB
g++-12 random_02 :heavy_check_mark: AC 66 ms 4 MB
g++-12 random_03 :heavy_check_mark: AC 7 ms 4 MB
g++-12 random_04 :heavy_check_mark: AC 7 ms 4 MB
g++-12 random_05 :heavy_check_mark: AC 6 ms 4 MB
g++-12 random_06 :heavy_check_mark: AC 7 ms 4 MB
g++-12 random_07 :heavy_check_mark: AC 7 ms 4 MB
g++-12 random_08 :heavy_check_mark: AC 7 ms 4 MB
g++-12 random_09 :heavy_check_mark: AC 7 ms 4 MB
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