Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/binomial_coefficient.test.cpp

Depends on

Code

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

#include "../../code/comb/exlucas.hpp"
#include "../../code/io/fastio.hpp"

int main() {
  u32 t, m;
  tifa_libs::fin >> t >> m;
  if (m == 1) {
    while (t--) tifa_libs::fout << "0\n";
  } else {
    tifa_libs::math::ExLucas mCn(m);
    while (t--) {
      i64 n, k;
      tifa_libs::fin >> n >> k;
      tifa_libs::fout << mCn(n, k) << '\n';
    }
  }
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/binomial_coefficient.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient"

#line 1 "src/code/comb/exlucas.hpp"



#line 1 "src/code/math/isqrt.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&&...) {};


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

namespace tifa_libs::math {

constexpr u32 isqrt(u64 x) {
  if (!x) return 0;
  int c = i32(std::bit_width(x) - 1) / 2, sh = 31 - c;
  u32 u = [](u64 x) {
    constexpr u8 TAB[192] = {128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145, 146, 147, 148, 149, 150, 151, 151, 152, 153, 154, 155, 156, 156, 157, 158, 159, 160, 160, 161, 162, 163, 164, 164, 165, 166, 167, 167, 168, 169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 179, 179, 180, 181, 181, 182, 183, 183, 184, 185, 186, 186, 187, 188, 188, 189, 190, 190, 191, 192, 192, 193, 194, 194, 195, 196, 196, 197, 198, 198, 199, 200, 200, 201, 201, 202, 203, 203, 204, 205, 205, 206, 206, 207, 208, 208, 209, 210, 210, 211, 211, 212, 213, 213, 214, 214, 215, 216, 216, 217, 217, 218, 219, 219, 220, 220, 221, 221, 222, 223, 223, 224, 224, 225, 225, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 255};
    u32 u = TAB[(x >> 56) - 64];
    u = (u << 7) + (u32)(x >> 41) / u;
    return (u << 15) + (u32)((x >> 17) / u);
  }(x << 2 * sh);
  u >>= sh;
  u -= (u64)u * u > x;
  return u;
}

}  // namespace tifa_libs::math


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



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



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

namespace tifa_libs::math {

// @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>
constexpr auto exgcd(T a, T b) {
  T x1 = 1, x2 = 0, x3 = 0, x4 = 1;
  while (b) {
    T c = a / b;
    std::tie(x1, x2, x3, x4, a, b) = std::make_tuple(x3, x4, x1 - x3 * c, x2 - x4 * c, b, a - b * c);
  }
  return std::make_tuple(to_uint_t<T>(a), x1, x2);
}

}  // 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, y] = exgcd(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {
namespace crt_impl_ {
constexpr std::optional<ptt<i64>> crt2(i64 a0, u64 m0, i64 a1, u64 m1) {
  if (m0 < m1) return crt2(a1, m1, a0, m0);
  auto [d, x] = inv_gcd(m0, m1);
  i64 a1_a0 = a1 - a0, a1_a0_d = a1_a0 / (i64)d;
  if (a1_a0 != a1_a0_d * (i64)d) return {};
  i64 m1_d = (i64)(m1 / d), k0 = (i64)x % m1_d * (a1_a0_d % m1_d) % m1_d;
  if (k0 < 0) k0 += m1_d;
  return std::make_pair(a0 + k0 * (i64)m0, (i64)m0 * m1_d);
}
}  // namespace crt_impl_

// Returns (remainder, modular)
constexpr std::optional<ptt<u64>> crt(vec<i64> const &a, vecu64 const &m) {
  if (a.size() != m.size()) return {};
  i64 A = 0;
  u64 M = 1;
  u32 n = (u32)a.size();
  for (u32 i = 0; i < n; ++i) {
    auto res = crt_impl_::crt2(safe_mod(a[i], m[i]), m[i], A, M);
    if (!res) return {};
    std::tie(A, M) = res.value();
  }
  return std::make_pair(A, M);
}

}  // namespace tifa_libs::math


#line 1 "src/code/comb/lucas_pp.hpp"



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



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



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

namespace tifa_libs::math {

constexpr u64 mul_mod_u(u64 a, u64 b, u64 mod) {
  if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
  else return (u64)((u128)a * b % mod);
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

constexpr u64 qpow_mod(u64 a, u64 b, u64 mod) {
  u64 res(1);
  for (a %= mod; b; b >>= 1, a = mul_mod_u(a, a, mod))
    if (b & 1) res = mul_mod_u(res, a, mod);
  return res;
}

}  // namespace tifa_libs::math


#line 1 "src/code/comb/gen_invseq.hpp"



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



#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/comb/gen_invseq.hpp"

namespace tifa_libs::math {

// i^{-1} for i in v
constexpr vecu64 gen_invseq(vecu64 const &v, u64 mod) {
  u32 n = (u32)v.size();
  if (n == 0) return {};
  if (n == 1) return {inverse(v[0], mod)};
  vecu64 ans(n);
  ans[0] = v[1];
  for (u32 i = 1; i < n; ++i) ans[i] = mul_mod_u(ans[i - 1], v[i], mod);
  u64 _ = inverse(ans.back(), mod);
  for (u32 i = n - 1; i; --i) {
    ans[i] = mul_mod_u(_, ans[i - 1], mod);
    _ = mul_mod_u(_, v[i], mod);
  }
  ans[0] = _;
  return ans;
}
// i^{-1} for i in v
template <class mint>
constexpr vec<mint> gen_invseq(vec<mint> const &v) {
  u32 n = (u32)v.size();
  vec<mint> ans(n);
  auto _ = gen_invseq(v, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/comb/lucas_pp.hpp"

namespace tifa_libs::math {

class LucasPP {
  u32 p, q;
  u64 m_;
  bool no_proot;
  vecu64 facp, ifacp;

 public:
  // mod = p ** q
  // @param p MUSU be prime
  constexpr LucasPP(u32 p, u32 q) : p(p), q(q) {
    assert(p <= 100'000'000 && q > 0);
    m_ = 1;
    while (q--) {
      m_ *= p;
      assert(m_ <= 100'000'000);
    }
    no_proot = (p == 2 && q >= 3);
    facp.resize(m_);
    facp[0] = facp[1] = 1;
    for (u32 i = 2; i < m_; ++i)
      if (i % p == 0) {
        facp[i] = facp[i - 1];
        facp[i + 1] = facp[i - 1] * (i + 1) % m_;
        ++i;
      } else facp[i] = facp[i - 1] * i % m_;
    ifacp = gen_invseq(facp, m_);
  }

  constexpr u64 mod() const { return m_; }

  constexpr u64 operator()(i64 m, i64 n) const {
    if (m < n || n < 0) return 0;
    i64 r = m - n;
    i32 e0 = 0, eq = 0;
    u32 i = 0;
    u64 res = 1;
    while (m) {
      res = res * facp[(u64)m % m_] % m_ * ifacp[(u64)n % m_] % m_ * ifacp[(u64)r % m_] % m_;
      m /= p;
      n /= p;
      r /= p;
      i32 eps = (i32)(m - n - r);
      if ((e0 += eps) >= (i32)q) return 0;
      if (++i >= q) eq += eps;
    }
    return (!no_proot && (eq & 1) ? m_ - res : res) * qpow_mod(p, (u32)e0, m_) % m_;
  }
};

}  // namespace tifa_libs::math


#line 7 "src/code/comb/exlucas.hpp"

namespace tifa_libs::math {

// Calculate binom(m, n) mod p, p can be ANY INTEGER
class ExLucas {
  u32 m_;
  vecu64 ms;
  vec<LucasPP> cs;

 public:
  explicit constexpr ExLucas(u32 md) : m_(md) {
    assert(md < 100'000'000);
    for (u32 i = 2, ed_ = isqrt(md); i <= ed_; ++i)
      if (md % i == 0) {
        u32 j = 0, k = 1;
        while (md % i == 0) {
          md /= i;
          ++j;
          k *= i;
        }
        ms.push_back(k);
        cs.emplace_back(i, j);
      }
    if (md > 1) {
      ms.push_back(md);
      cs.emplace_back(md, 1);
    }
  }

  constexpr u64 operator()(i64 m, i64 n) const {
    if (m_ == 1 || m < n || n < 0) return 0;
    vec<i64> b;
    b.reserve(cs.size());
    for (auto const &i : cs) b.push_back((i64)i(m, n));
    return crt(b, ms)->first;
  }
};

}  // namespace tifa_libs::math


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



#line 1 "src/code/fast/u32tostr.hpp"



#line 5 "src/code/fast/u32tostr.hpp"

namespace tifa_libs {

constexpr u32 u32tostr_si16(u64 x, char *s) {
  if (x <= 9) {
    *s = (char)(x | 0x30);
    return 1;
  } else if (x <= 99) {
    u64 low = x;
    u64 ll = ((low * 103) >> 9) & 0x1E;
    low += ll * 3;
    ll = ((low & 0xF0) >> 4) | ((low & 0x0F) << 8);
    *(u16 *)s = (u16)(ll | 0x3030);
    return 2;
  }
  return 0;
}
constexpr u32 u32tostr_si32(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 99) return u32tostr_si16(x, s);
  low = x;
  digits = (low > 999) ? 4 : 3;
  ll = ((low * 5243) >> 19) & 0xFF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x1E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F0) << 28) | (low & 0x000F000F) << 40;
  ll |= 0x3030303000000000;
  u8 *p = (u8 *)&ll;
  if (digits == 4) *(u32 *)s = *(u32 *)(&p[4]);
  else {
    *(u16 *)s = *(u16 *)(&p[5]);
    *(((u8 *)s) + 2) = p[7];
  }

  return digits;
}

constexpr u32 u32tostr(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 9999) return u32tostr_si32(x, s);
  if (x < 100000000) {
    if ((low = x) > 999999) digits = (low > 9999999) ? 8 : 7;
    else digits = (low > 99999) ? 6 : 5;
  } else {
    u64 high = (x * 0x55E63B89) >> 57;
    low = x - (high * 100000000);
    digits = u32tostr_si16(high, s);
    digits += 8;
  }

  ll = (low * 109951163) >> 40;
  (low -= ll * 10000) |= ll << 32;
  ll = ((low * 5243) >> 19) & 0x000000FF000000FF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x001E001E001E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F000F000F0) >> 4) | (low & 0x000F000F000F000F) << 8;
  ll = (ll >> 32) | (ll << 32) | 0x3030303030303030;

  if (digits >= 8) memcpy(s + digits - 8, &ll, 8);
  else {
    u32 d = digits;
    char *s1 = s, *pll = &(((char *)&ll)[8 - digits]);
    if (d >= 4) {
      memcpy(s1, pll, 4);
      s1 += 4, pll += 4, d -= 4;
    }
    if (d >= 2) {
      memcpy(s1, pll, 2);
      s1 += 2, pll += 2, d -= 2;
    }
    if (d > 0) *(u8 *)s1 = *(u8 *)pll;
  }
  return digits;
}

}  // namespace tifa_libs


#line 6 "src/code/io/fastio.hpp"

namespace tifa_libs {
namespace fastio_impl_ {
//! UB if EOF occured during reading
template <u32 BUF>
class fastin {
  char bf_[BUF], *now_ = bf_, *end_ = bf_;
  FILE *f_;

 public:
  explicit fastin(FILE *f = stdin) : f_(f) {}

  char get() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_)++; }
  char peek() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_); }
  void rebind(FILE *f) {
    f_ = f;
    now_ = end_ = bf_;
  }

  bool iseof() { return peek() == EOF; }

  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    bool is_neg = false;
    char ch = get();
    while (!isdigit(ch)) {
      is_neg |= ch == '-';
      ch = get();
    }
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    if (is_neg) n = -n;
    return *this;
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    char ch = get();
    while (!isdigit(ch)) ch = get();
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    return *this;
  }
  template <mint_c T>
  fastin &read(T &n) {
    decltype(std::declval<T>().sval()) x;
    read(x);
    n = T(x);
    return *this;
  }
  //! ignore cntrl and space
  template <char_c T>
  fastin &read(T &n) {
    while (!isgraph(n = get()));
    return *this;
  }
  fastin &read(char *n) {
    char *n_ = n;
    while (!isgraph(*n_ = get()));
    while (isgraph(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &read(strn &n) {
    n.clear();
    char n_;
    while (!isgraph(n_ = get()));
    n.push_back(n_);
    while (isgraph(n_ = get())) n.push_back(n_);
    return *this;
  }
  template <class T, class U>
  fastin &read(std::pair<T, U> &p) { return read(p.first).read(p.second); }
  template <class... Ts>
  fastin &read(std::tuple<Ts...> &p) {
    std::apply([&](Ts &...targs) { ((read(targs)), ...); }, p);
    return *this;
  }
  template <container_c T>
  fastin &read(T &p) {
    if (p.begin() == p.end()) return *this;
    for (auto &i : p) read(i);
    return *this;
  }

  fastin &getline(char *n) {
    char *n_ = n;
    while (!isprint(*n_ = get()));
    while (isprint(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &getline(strn &n) {
    char n_;
    while (!isprint(n_ = get()));
    n.push_back(n_);
    while (isprint(n_ = get())) n.push_back(n_);
    return *this;
  }

  //! NOT ignore cntrl and space
  template <char_c T>
  fastin &strict_read(T &n) {
    n = get();
    return *this;
  }

  template <class T>
  fastin &operator>>(T &val) { return read(val); }
};
template <u32 BUF, u32 INTBUF>
class fastout {
  char int_bf_[INTBUF], *now_ib_ = int_bf_;

  FILE *f_;
  char *now_, bf_[BUF];
  const char *const end_ = bf_ + BUF;

 public:
  explicit fastout(FILE *file = stdout) : f_(file), now_(bf_) {}

  fastout &operator=(fastout const &r) {
    f_ = r.f_;
    now_ = bf_ + (r.now_ - r.bf_);
    memcpy(bf_, r.bf_, sizeof(*bf_) * (r.now_ - r.bf_));
    return *this;
  }
  fastout(fastout const &r) { *this = r; }

  ~fastout() { flush(); }

  void flush() {
    fwrite(bf_, 1, usz(now_ - bf_), f_);
    now_ = bf_;
  }
  void rebind(FILE *file) { f_ = file; }

  template <char_c T>
  fastout &write(T const &n) {
    if (now_ == end_) flush();
    *(now_++) = n;
    return *this;
  }
  fastout &write(const char *n) {
    usz len = strlen(n), l_;
    const char *n_ = n;
    while (now_ + len >= end_) {
      memcpy(now_, n_, l_ = usz(end_ - now_));
      now_ += l_;
      n_ += l_;
      len -= l_;
      flush();
    }
    memcpy(now_, n_, len);
    now_ += len;
    return *this;
  }
  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if (n < 0) {
      write('-');
      n = -n;
    }
    return write(to_uint_t<T>(n));
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if constexpr (sizeof(T) <= 4) {
      memset(now_ib_ = int_bf_, 0, 11);
      u32tostr(n, now_ib_);
      return write(now_ib_);
    }
    now_ib_ = int_bf_ + INTBUF - 1;
    do {
      *(--(now_ib_)) = char(n % 10) | '0';
    } while (n /= 10);
    return write(now_ib_);
  }
  template <mint_c T>
  fastout &write(T n) { return write(n.val()); }
  fastout &write(strn const &str) { return write(str.c_str()); }
  template <class T, class U>
  fastout &write(std::pair<T, U> const &p) { return write(p.first).space().write(p.second); }
  template <class... Ts>
  fastout &write(std::tuple<Ts...> const &p) {
    std::apply(
        [&](Ts const &...targs) {
          usz n{0};
          ((write(targs).space_if(++n != sizeof...(Ts))), ...);
        },
        p);
    return *this;
  }
  template <container_c T>
  fastout &write(T const &p) {
    if (p.begin() == p.end()) return *this;
    auto it = p.begin();
    write(*it++);
    for (; it != p.end(); ++it) space().write(*it);
    return *this;
  }

  fastout &linebreak() { return write('\n'); }
  fastout &linebreak_if(bool flag) { return flag ? linebreak() : *this; }
  fastout &space() { return write(' '); }
  fastout &space_if(bool flag) { return flag ? space() : *this; }

  template <class T>
  fastout &operator<<(T const &val) { return write(val); }
};
}  // namespace fastio_impl_

inline fastio_impl_::fastin<0x200005> fin;
inline fastio_impl_::fastout<0x200005, 41> fout;

}  // namespace tifa_libs


#line 5 "src/test_cpverifier/library-checker/binomial_coefficient.test.cpp"

int main() {
  u32 t, m;
  tifa_libs::fin >> t >> m;
  if (m == 1) {
    while (t--) tifa_libs::fout << "0\n";
  } else {
    tifa_libs::math::ExLucas mCn(m);
    while (t--) {
      i64 n, k;
      tifa_libs::fin >> n >> k;
      tifa_libs::fout << mCn(n, k) << '\n';
    }
  }
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 example_00 :heavy_check_mark: AC 10 ms 6 MB
g++-12 example_01 :heavy_check_mark: AC 9 ms 6 MB
g++-12 m_1_n_max_00 :heavy_check_mark: AC 10 ms 6 MB
g++-12 m_510510_n_max_00 :heavy_check_mark: AC 234 ms 8 MB
g++-12 m_524288_n_max_00 :heavy_check_mark: AC 279 ms 16 MB
g++-12 m_720720_n_max_00 :heavy_check_mark: AC 258 ms 8 MB
g++-12 m_n_510510_00 :heavy_check_mark: AC 137 ms 7 MB
g++-12 m_n_524288_00 :heavy_check_mark: AC 119 ms 16 MB
g++-12 m_n_720720_00 :heavy_check_mark: AC 156 ms 8 MB
g++-12 m_n_999983_00 :heavy_check_mark: AC 51 ms 23 MB
g++-12 m_prime_n_max_00 :heavy_check_mark: AC 48 ms 8 MB
g++-12 m_prime_n_max_01 :heavy_check_mark: AC 46 ms 7 MB
g++-12 m_prime_n_max_02 :heavy_check_mark: AC 46 ms 7 MB
g++-12 m_prime_n_max_03 :heavy_check_mark: AC 65 ms 17 MB
g++-12 m_prime_n_max_04 :heavy_check_mark: AC 64 ms 19 MB
g++-12 max_random_00 :heavy_check_mark: AC 189 ms 8 MB
g++-12 max_random_01 :heavy_check_mark: AC 208 ms 7 MB
g++-12 max_random_02 :heavy_check_mark: AC 220 ms 7 MB
g++-12 max_random_03 :heavy_check_mark: AC 206 ms 8 MB
g++-12 max_random_04 :heavy_check_mark: AC 212 ms 8 MB
g++-12 n_small_00 :heavy_check_mark: AC 42 ms 8 MB
g++-12 n_small_01 :heavy_check_mark: AC 67 ms 8 MB
g++-12 n_small_02 :heavy_check_mark: AC 80 ms 7 MB
g++-12 n_small_03 :heavy_check_mark: AC 63 ms 8 MB
g++-12 n_small_04 :heavy_check_mark: AC 98 ms 8 MB
g++-12 n_small_05 :heavy_check_mark: AC 67 ms 7 MB
g++-12 n_small_06 :heavy_check_mark: AC 69 ms 7 MB
g++-12 n_small_07 :heavy_check_mark: AC 47 ms 9 MB
g++-12 n_small_08 :heavy_check_mark: AC 78 ms 7 MB
g++-12 n_small_09 :heavy_check_mark: AC 61 ms 8 MB
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