Tifa's CP Library

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

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#ifndef TIFALIBS_COMB_BALL_BOX_DIL
#define TIFALIBS_COMB_BALL_BOX_DIL

#include "gen_stirling2_row.hpp"

namespace tifa_libs::math {

template <class poly>
constexpr auto ball_box_dil(u32 ball, u32 box, poly const& s2r) { return box > ball ? 0 : s2r[box]; }
template <class poly>
constexpr auto ball_box_dil(u32 ball, u32 box) { return ball_box_dil<poly>(ball, box, gen_stirling2_row<poly>(ball)); }

}  // namespace tifa_libs::math

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



#line 1 "src/code/comb/gen_stirling2_row.hpp"



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



#line 1 "src/code/math/mul_mod_u.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/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 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
constexpr vecu64 gen_inv(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(mod - mod / i, ans[mod % i], mod);
  return ans;
}
// i^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_inv(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_inv(n, mint::mod());
  for (u32 i = 0; i < n; ++i) 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
constexpr vecu64 gen_ifact(u32 n, u64 mod, vecu64 inv) {
  for (u32 i = 2; i < n; ++i) inv[i] = mul_mod_u(inv[i], inv[i - 1], mod);
  return inv;
}
// (i!)^{-1} from i=0..n-1
constexpr vecu64 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>
constexpr vec<mint> gen_ifact(u32 n, vec<mint> inv) {
  for (u32 i = 2; i < n; ++i) inv[i] *= inv[i - 1];
  return inv;
}
// (i!)^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_ifact(u32 n) { return gen_ifact(n, gen_inv<mint>(n)); }

}  // namespace tifa_libs::math


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



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



#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 5 "src/code/comb/gen_pows.hpp"

namespace tifa_libs::math {

// i^{b} from i=0..n-1
constexpr vecu64 gen_pows(u32 n, u64 b, u64 mod) {
  vecu64 ans(n);
  if (!n) return {};
  if (!b) ans[0] = 1;
  if (n == 1) return ans;
  ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = qpow_mod(i, b, mod);
  return ans;
}
// i^{b} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_pows(u32 n, u64 b) {
  vec<mint> ans(n);
  auto _ = gen_pows(n, b, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/comb/gen_stirling2_row.hpp"

namespace tifa_libs::math {

// stirling2[i] = {n \\brace i}, i=0,1,...,n
template <class poly>
constexpr poly gen_stirling2_row(u32 n, vecu64 const& pows, vecu64 const& ifact) {
  using mint = typename poly::value_type;
  if (!n) return poly{1};
  u64 mod = mint::mod();
  poly a(n + 1), b(n + 1);
  for (u32 i = 1; i <= n; ++i) a[i] = mul_mod_u(pows[i], ifact[i], mod);
  for (u32 i = 0; i <= n; ++i) b[i] = ((i & 1) ? mod - ifact[i] : ifact[i]);
  a *= b;
  a.resize(n + 1);
  return a;
}
// stirling2[i] = {n \\brace i}, i=0,1,...,n
template <class poly>
constexpr poly gen_stirling2_row(u32 n) {
  using mint = typename poly::value_type;
  return gen_stirling2_row<poly>(n, gen_pows(n + 1, n, mint::mod()), gen_ifact(n + 1, mint::mod()));
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <class poly>
constexpr auto ball_box_dil(u32 ball, u32 box, poly const& s2r) { return box > ball ? 0 : s2r[box]; }
template <class poly>
constexpr auto ball_box_dil(u32 ball, u32 box) { return ball_box_dil<poly>(ball, box, gen_stirling2_row<poly>(ball)); }

}  // namespace tifa_libs::math


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