Luzhiled's Library

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:x: test/verify/yukicoder-502.test.cpp

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Code

#define PROBLEM "https://yukicoder.me/problems/no/502"

#include "../../template/template.hpp"

#include "../../math/combinatorics/mod-int.hpp"
#include "../../math/combinatorics/factorial.hpp"

#include "../../math/fft/arbitrary-mod-convolution.hpp"

const int MOD = (int) (1e9 + 7);
using mint = ModInt< MOD >;

int main() {
  int N;
  cin >> N;
  ArbitraryModConvolution< mint > fft;
  auto f = [&](vector< mint > &a, vector< mint > &b) { return fft.multiply(a, b); };
  cout << factorial< mint >(N, f) << "\n";
}
#line 1 "test/verify/yukicoder-502.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/502"

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yukicoder-502.test.cpp"

#line 1 "math/combinatorics/mod-int.hpp"
template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< mod >;
#line 1 "math/combinatorics/enumeration.hpp"
/**
 * @brief Enumeration(組み合わせ)
 */
template< typename T >
struct Enumeration {
private:
  static vector< T > _fact, _finv, _inv;

  inline static void expand(size_t sz) {
    if(_fact.size() < sz + 1) {
      int pre_sz = max(1, (int) _fact.size());
      _fact.resize(sz + 1, T(1));
      _finv.resize(sz + 1, T(1));
      _inv.resize(sz + 1, T(1));
      for(int i = pre_sz; i <= (int) sz; i++) {
        _fact[i] = _fact[i - 1] * T(i);
      }
      _finv[sz] = T(1) / _fact[sz];
      for(int i = (int) sz - 1; i >= pre_sz; i--) {
        _finv[i] = _finv[i + 1] * T(i + 1);
      }
      for(int i = pre_sz; i <= (int) sz; i++) {
        _inv[i] = _finv[i] * _fact[i - 1];
      }
    }
  }

public:
  explicit Enumeration(size_t sz = 0) { expand(sz); }

  static inline T fact(int k) {
    expand(k);
    return _fact[k];
  }

  static inline T finv(int k) {
    expand(k);
    return _finv[k];
  }

  static inline T inv(int k) {
    expand(k);
    return _inv[k];
  }

  static T P(int n, int r) {
    if(r < 0 || n < r) return 0;
    return fact(n) * finv(n - r);
  }

  static T C(int p, int q) {
    if(q < 0 || p < q) return 0;
    return fact(p) * finv(q) * finv(p - q);
  }

  static T H(int n, int r) {
    if(n < 0 || r < 0) return 0;
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

template< typename T >
vector< T > Enumeration< T >::_fact = vector< T >();
template< typename T >
vector< T > Enumeration< T >::_finv = vector< T >();
template< typename T >
vector< T > Enumeration< T >::_inv = vector< T >();
#line 2 "math/combinatorics/sample-point-shift.hpp"

/**
 * @brief Sample Point Shift(標本点シフト)
 */
template< typename Mint, typename F >
vector< Mint > sample_point_shift(const vector< Mint > &ys, const Mint &m, const F &multiply) {
  Enumeration< Mint > comb;
  int d = (int) ys.size() - 1;
  vector< Mint > f(d + 1), g(d * 2 + 1);
  for(int i = 0; i <= d; i++) {
    f[i] = ys[i] * comb.finv(i) * comb.finv(d - i);
    if((d - i) & 1) f[i] = -f[i];
  }
  for(int i = 0; i <= 2 * d; i++) {
    g[i] = Mint(1) / (m - d + i);
  }
  auto h = multiply(f, g);
  Mint coef = 1;
  for(int i = 0; i <= d; i++) {
    coef *= (m - d + i);
  }
  for(int i = 0; i <= d; i++) {
    h[i + d] *= coef;
    coef *= (m + i + 1) * g[i];
  }
  return vector< Mint >{begin(h) + d, begin(h) + 2 * d + 1};
}
#line 2 "math/combinatorics/factorial.hpp"

/**
 * @brief Factorial(階乗)
 */
template< typename Mint, typename F >
Mint factorial(int64_t n, const F& multiply) {
  if(n <= 1) return 1;
  if(n >= Mint::get_mod()) return 0;
  int64_t v = 1;
  while(v * v < n) v *= 2;
  Mint iv = Mint(1) / v;
  vector< Mint > G{1, v + 1};
  for(int64_t d = 1; d != v; d <<= 1) {
    vector< Mint > G1 = sample_point_shift(G, Mint(d) * iv, multiply);
    vector< Mint > G2 = sample_point_shift(G, Mint(d * v + v) * iv, multiply);
    vector< Mint > G3 = sample_point_shift(G, Mint(d * v + d + v) * iv, multiply);
    for(int i = 0; i <= d; i++) G[i] *= G1[i], G2[i] *= G3[i];
    copy(begin(G2), end(G2) - 1, back_inserter(G));
  }
  Mint res = 1;
  int64_t i = 0;
  while(i + v <= n) res *= G[i / v], i += v;
  while(i < n) res *= ++i;
  return res;
}
#line 7 "test/verify/yukicoder-502.test.cpp"

#line 1 "math/fft/fast-fourier-transform.hpp"
namespace FastFourierTransform {
  using real = double;

  struct C {
    real x, y;

    C() : x(0), y(0) {}

    C(real x, real y) : x(x), y(y) {}

    inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

    inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

    inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

    inline C conj() const { return C(x, -y); }
  };

  const real PI = acosl(-1);
  int base = 1;
  vector< C > rts = { {0, 0},
                     {1, 0} };
  vector< int > rev = {0, 1};


  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while(base < nbase) {
      real angle = PI * 2.0 / (1 << (base + 1));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        real angle_i = angle * (2 * i + 1 - (1 << base));
        rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
      }
      ++base;
    }
  }

  void fft(vector< C > &a, int n) {
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          C z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }

  vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
    int need = (int) a.size() + (int) b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < sz; i++) {
      int x = (i < (int) a.size() ? a[i] : 0);
      int y = (i < (int) b.size() ? b[i] : 0);
      fa[i] = C(x, y);
    }
    fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
      fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
      fa[i] = z;
    }
    for(int i = 0; i < (sz >> 1); i++) {
      C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
      C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
      fa[i] = A0 + A1 * s;
    }
    fft(fa, sz >> 1);
    vector< int64_t > ret(need);
    for(int i = 0; i < need; i++) {
      ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
  }
};
#line 2 "math/fft/arbitrary-mod-convolution.hpp"

/*
 * @brief Arbitrary Mod Convolution(任意mod畳み込み)
 */
template< typename T >
struct ArbitraryModConvolution {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolution() = default;

  static vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
    if(need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < a.size(); i++) {
      fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
    }
    fft(fa, sz);
    vector< C > fb(sz);
    if(a == b) {
      fb = fa;
    } else {
      for(int i = 0; i < b.size(); i++) {
        fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if(i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    vector< T > ret(need);
    for(int i = 0; i < need; i++) {
      int64_t aa = llround(fa[i].x);
      int64_t bb = llround(fb[i].x);
      int64_t cc = llround(fa[i].y);
      aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
      ret[i] = aa + (bb << 15) + (cc << 30);
    }
    return ret;
  }
};
#line 9 "test/verify/yukicoder-502.test.cpp"

const int MOD = (int) (1e9 + 7);
using mint = ModInt< MOD >;

int main() {
  int N;
  cin >> N;
  ArbitraryModConvolution< mint > fft;
  auto f = [&](vector< mint > &a, vector< mint > &b) { return fft.multiply(a, b); };
  cout << factorial< mint >(N, f) << "\n";
}
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