Tifa's CP Library

:heavy_check_mark: ball_box_ddm (src/code/comb/ball_box_ddm.hpp)

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#ifndef TIFALIBS_COMB_BALL_BOX_DDM
#define TIFALIBS_COMB_BALL_BOX_DDM

#include "binom.hpp"

namespace tifa_libs::math {

template <class mint>
CEXP mint ball_box_ddm(u32 ball, u32 box, Binom<mint> CR binom) { return binom.mPn(box, ball); }

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/comb/ball_box_ddm.hpp"



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



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



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



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

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

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

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
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 T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
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, 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>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

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

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


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

namespace tifa_libs {

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

template <class T>
concept container_c = iterable_c<T> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;

template <class T>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
CEXP 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>
concept dft_c = requires(T x, vec<TPN T::data_t> v, u32 n) {
  { x.size() } -> std::same_as<u32>;
  x.bzr(n);
  x.dif(v, n);
  x.dit(v, n);
};

template <class T>
concept ntt_c = dft_c<T> && requires(T x) {
  T::max_size;
  T::G;
};

template <class T>
CEXP 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 = TPN 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 = TPN to_uint<T>::type;

}  // namespace tifa_libs


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



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



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



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

namespace tifa_libs::math {

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

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

CEXP i64 mul_mod_s(i64 a, i64 b, u64 mod) {
  if (std::bit_width((u64)abs(a)) + std::bit_width((u64)abs(b)) < 64) return safe_mod(a * b % (i64)mod, mod);
  return safe_mod((i64)((i128)a * b % mod), mod);
}
CEXP u64 mul_mod_u(u64 a, u64 b, u64 mod) {
  if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
  return (u64)((u128)a * b % mod);
}

}  // namespace tifa_libs::math


#line 5 "src/code/comb/gen_fact.hpp"

namespace tifa_libs::math {

// i! from i=0..n-1
CEXP vecuu gen_fact(u32 n, u64 mod) {
  if (n <= 1) return vecuu(n, 1);
  vecuu ans(n);
  ans[0] = ans[1] = 1;
  flt_ (u32, i, 2, n) ans[i] = mul_mod_u(ans[i - 1], i, mod);
  return ans;
}
// i! from i=0..n-1
template <class mint>
CEXP vec<mint> gen_fact(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_fact(n, mint::mod());
  flt_ (u32, i, 0, n) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


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



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



#line 5 "src/code/comb/gen_inv.hpp"

namespace tifa_libs::math {

// i^{-1} from i=0..n-1
CEXP vecuu gen_inv(u32 n, u64 mod) {
  if (n <= 1) return vecuu(n, 1);
  vecuu ans(n);
  ans[0] = ans[1] = 1;
  flt_ (u32, i, 2, n) ans[i] = mul_mod_u(mod - mod / i, ans[mod % i], mod);
  return ans;
}
// i^{-1} from i=0..n-1
template <class mint>
CEXP vec<mint> gen_inv(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_inv(n, mint::mod());
  flt_ (u32, i, 0, n) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

// (i!)^{-1} from i=0..n-1
CEXP vecuu gen_ifact(u32 n, u64 mod, vecuu inv) {
  flt_ (u32, i, 2, n) inv[i] = mul_mod_u(inv[i], inv[i - 1], mod);
  return inv;
}
// (i!)^{-1} from i=0..n-1
CEXP vecuu gen_ifact(u32 n, u64 mod) { return gen_ifact(n, mod, gen_inv(n, mod)); }
// (i!)^{-1} from i=0..n-1
template <class mint>
CEXP vec<mint> gen_ifact(u32 n, vec<mint> inv) {
  flt_ (u32, i, 2, n) inv[i] *= inv[i - 1];
  return inv;
}
// (i!)^{-1} from i=0..n-1
template <class mint>
CEXP vec<mint> gen_ifact(u32 n) { return gen_ifact(n, gen_inv<mint>(n)); }

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <class mint>
struct Binom {
  vec<mint> fact, ifact;

  static CEXP u64 mod() { return mint::mod(); }
  CEXPE Binom(u32 max_m = 0) : fact(gen_fact<mint>(std::min((u32)mod(), max_m + 1))), ifact(gen_ifact<mint>(std::min((u32)mod(), max_m + 1))) {}

  // $\binom{m}{n}$
  template <uint_c T>
  CEXP mint mCn(T m, T n) const { return m < n ? 0 : mPn(m, n) * ifact[(usz)n]; }
  // $\binom{m}{n}$
  template <sint_c T>
  CEXP mint mCn(T m, T n) const { return m < n || n < 0 ? 0 : mCn(to_uint_t<T>(m), to_uint_t<T>(n)); }
  //! mint::mod() must be prime
  template <int_c T>
  CEXP mint lucas(T m, T n) const {
    assert(mint::mod() > 1);
    auto f = [this](auto &&f, auto m, auto n) -> mint { return n == 0 ? 1 : this->mCn(m % mod(), n % mod()) * f(f, m / mod(), n / mod()); };
    return m < n || n < 0 ? 0 : f(f, to_uint_t<T>(m), to_uint_t<T>(n));
  }
  // $\binom{m}{n} \cdot n!$
  template <uint_c T>
  CEXP mint mPn(T m, T n) const { return m < n ? 0 : fact[(usz)m] * ifact[(usz)(m - n)]; }
  // $\binom{m}{n} \cdot n!$
  template <sint_c T>
  CEXP mint mPn(T m, T n) const { return m < n || n < 0 ? 0 : mPn(to_uint_t<T>(m), to_uint_t<T>(n)); }
  // $[x^n] \frac{1}{(1-x)^m}$
  template <uint_c T>
  CEXP mint mHn(T m, T n) const { return n <= 0 ? n == 0 : mCn(m + n - 1, n); }
  // $[x^n] \frac{1}{(1-x)^m}$
  template <sint_c T>
  CEXP mint mHn(T m, T n) const { return m < 0 || n <= 0 ? n == 0 : mHn(to_uint_t<T>(m), to_uint_t<T>(n)); }
};

}  // namespace tifa_libs::math


#line 5 "src/code/comb/ball_box_ddm.hpp"

namespace tifa_libs::math {

template <class mint>
CEXP mint ball_box_ddm(u32 ball, u32 box, Binom<mint> CR binom) { return binom.mPn(box, ball); }

}  // namespace tifa_libs::math


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