結果

問題 No.502 階乗を計算するだけ
ユーザー Min_25Min_25
提出日時 2017-04-08 11:52:25
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 270 ms / 1,000 ms
コード長 21,706 bytes
コンパイル時間 3,777 ms
コンパイル使用メモリ 133,984 KB
実行使用メモリ 15,908 KB
最終ジャッジ日時 2023-09-24 23:19:54
合計ジャッジ時間 7,730 ms
ジャッジサーバーID
(参考情報)
judge13 / judge14
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
4,380 KB
testcase_01 AC 1 ms
4,376 KB
testcase_02 AC 2 ms
4,376 KB
testcase_03 AC 2 ms
4,380 KB
testcase_04 AC 1 ms
4,380 KB
testcase_05 AC 1 ms
4,376 KB
testcase_06 AC 2 ms
4,376 KB
testcase_07 AC 1 ms
4,376 KB
testcase_08 AC 1 ms
4,376 KB
testcase_09 AC 1 ms
4,376 KB
testcase_10 AC 2 ms
4,380 KB
testcase_11 AC 1 ms
4,380 KB
testcase_12 AC 1 ms
4,376 KB
testcase_13 AC 2 ms
4,376 KB
testcase_14 AC 1 ms
4,376 KB
testcase_15 AC 2 ms
4,376 KB
testcase_16 AC 1 ms
4,380 KB
testcase_17 AC 1 ms
4,380 KB
testcase_18 AC 2 ms
4,380 KB
testcase_19 AC 1 ms
4,380 KB
testcase_20 AC 2 ms
4,376 KB
testcase_21 AC 1 ms
4,376 KB
testcase_22 AC 5 ms
9,884 KB
testcase_23 AC 2 ms
4,376 KB
testcase_24 AC 5 ms
9,836 KB
testcase_25 AC 2 ms
4,376 KB
testcase_26 AC 3 ms
4,376 KB
testcase_27 AC 2 ms
4,376 KB
testcase_28 AC 3 ms
4,380 KB
testcase_29 AC 3 ms
4,380 KB
testcase_30 AC 5 ms
9,884 KB
testcase_31 AC 3 ms
4,380 KB
testcase_32 AC 242 ms
14,908 KB
testcase_33 AC 262 ms
15,336 KB
testcase_34 AC 216 ms
14,260 KB
testcase_35 AC 110 ms
12,436 KB
testcase_36 AC 256 ms
15,160 KB
testcase_37 AC 229 ms
14,552 KB
testcase_38 AC 267 ms
15,376 KB
testcase_39 AC 261 ms
14,960 KB
testcase_40 AC 86 ms
11,716 KB
testcase_41 AC 270 ms
15,908 KB
testcase_42 AC 2 ms
4,380 KB
testcase_43 AC 1 ms
4,376 KB
testcase_44 AC 2 ms
4,376 KB
testcase_45 AC 2 ms
4,376 KB
testcase_46 AC 1 ms
4,380 KB
testcase_47 AC 2 ms
4,376 KB
testcase_48 AC 1 ms
4,380 KB
testcase_49 AC 2 ms
4,376 KB
testcase_50 AC 1 ms
4,376 KB
testcase_51 AC 2 ms
4,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")

#include <cstdio>
#include <cassert>
#include <cmath>
#include <cstring>

#include <algorithm>
#include <iostream>
#include <vector>
#include <functional>

#ifdef __x86_64__
#define NTT64
#endif

#define _rep(_1, _2, _3, _4, name, ...) name
#define rep2(i, n) rep3(i, 0, n)
#define rep3(i, a, b) rep4(i, a, b, 1)
#define rep4(i, a, b, c) for (int i = int(a); i < int(b); i += int(c))
#define rep(...) _rep(__VA_ARGS__, rep4, rep3, rep2, _)(__VA_ARGS__)

using namespace std;

using i64 = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using f80 = long double;

namespace ntt {

#ifdef NTT64
  using word_t = u64;
  using dword_t = __uint128_t;
#else
  using word_t = u32;
  using dword_t = u64;
#endif
static const int word_bits = 8 * sizeof(word_t);

template <word_t mod, word_t prim_root>
class Mod {
private:
  static constexpr word_t mul_inv(word_t n, int e=6, word_t x=1) {
    return e == 0 ? x : mul_inv(n, e-1, x*(2-x*n));
  }
public:
  static constexpr word_t inv = mul_inv(mod);
  static constexpr word_t r2 = -dword_t(mod) % mod;
  static constexpr int level = __builtin_ctzll(mod - 1);
  static_assert(inv * mod == 1, "invalid 1/M modulo 2^@.");

  Mod() {}
  Mod(word_t n) : x(init(n)) {};
  static word_t modulus() { return mod; }
  static word_t init(word_t w) { return reduce(dword_t(w) * r2); }
  static word_t reduce(const dword_t w) { return word_t(w >> word_bits) + mod - word_t((dword_t(word_t(w) * inv) * mod) >> word_bits); }
  static Mod omega() { return Mod(prim_root).pow((mod - 1) >> level); }
  Mod& operator += (Mod rhs) { this->x += rhs.x; return *this; }
  Mod& operator -= (Mod rhs) { this->x += 3 * mod - rhs.x; return *this; }
  Mod& operator *= (Mod rhs) { this->x = reduce(dword_t(this->x) * rhs.x); return *this; }
  Mod operator + (Mod rhs) const { return Mod(*this) += rhs; }
  Mod operator - (Mod rhs) const { return Mod(*this) -= rhs; }
  Mod operator * (Mod rhs) const { return Mod(*this) *= rhs; }
  word_t get() const { return reduce(this->x) % mod; }
  void set(word_t n) const { this->x = n; }
  Mod pow(word_t exp) const {
    Mod ret = Mod(1);
    for (Mod base = *this; exp; exp >>= 1, base *= base) if (exp & 1) ret *= base;
    return ret;
  }
  Mod inverse() const { return pow(mod - 2); }
  friend ostream& operator << (ostream& os, const Mod& m) { return os << m.get(); }
  static void debug() {
    printf("%llu %llu %llu %llu\n", mod, inv, r2, omega().get());
  }
  word_t x;
};

const int size = 1 << 24;

#ifdef NTT64
  using m64_1 = ntt::Mod<709143768229478401, 31>;
  using m64_2 = ntt::Mod<711416664922521601, 19>; // <= 712e15 (sub.D = 3)
  m64_1 f1[size], g1[size];
  m64_2 f2[size], g2[size];
#else
  using m32_1 = ntt::Mod<138412033, 5>;
  using m32_2 = ntt::Mod<155189249, 6>;
  using m32_3 = ntt::Mod<163577857, 23>; // <=  16579e4 (sub.D = 3)
  m32_1 f1[size], g1[size];
  m32_2 f2[size], g2[size];
  m32_3 f3[size], g3[size];
#endif

template <typename mod_t>
void convolve(mod_t* A, int s1, mod_t* B, int s2, bool cyclic=false) {
  int s = (cyclic ? max(s1, s2) : s1 + s2 - 1);
  int size = 1;
  while (size < s) size <<= 1;
  mod_t roots[mod_t::level] = { mod_t::omega() };
  rep(i, 1, mod_t::level) roots[i] = roots[i - 1] * roots[i - 1];
  fill(A + s1, A + size, 0); ntt_dit4(A, size, 1, roots);
  if (A == B && s1 == s2) {
    rep(i, size) A[i] *= A[i];
  } else {
    fill(B + s2, B + size, 0); ntt_dit4(B, size, 1, roots);
    rep(i, size) A[i] *= B[i];
  }
  ntt_dit4(A, size, -1, roots);
  mod_t inv = mod_t(size).inverse();
  rep(i, cyclic ? size : s) A[i] *= inv;
}

template <typename mod_t>
void rev_permute(mod_t* A, int n) {
  int r = 0, nh = n >> 1;
  rep(i, 1, n) {
    for (int h = nh; !((r ^= h) & h); h >>= 1);
    if (r > i) swap(A[i], A[r]);
  }
}

template <typename mod_t>
void ntt_dit4(mod_t* A, int n, int sign, mod_t* roots) {
  rev_permute(A, n);
  int logn = __builtin_ctz(n);
  assert(logn <= mod_t::level);

  if (logn & 1) rep(i, 0, n, 2) {
    mod_t a = A[i], b = A[i + 1];
    A[i] = a + b; A[i + 1] = a - b;
  }
  mod_t imag = roots[mod_t::level - 2];
  if (sign < 0) imag = imag.inverse();

  mod_t one = mod_t(1);
  rep(e, 2 + (logn & 1), logn + 1, 2) {
    const int m = 1 << e;
    const int m4 = m >> 2;
    mod_t dw = roots[mod_t::level - e];
    if (sign < 0) dw = dw.inverse();

    const int block_size = min(n, max(m, (1 << 15) / int(sizeof(A[0]))));
    rep(k, 0, n, block_size) {
      mod_t w = one, w2 = one, w3 = one;
      rep(j, m4) {
        rep(i, k + j, k + block_size, m) {
          mod_t a0 = A[i + m4 * 0] * one, a2 = A[i + m4 * 1] * w2;
          mod_t a1 = A[i + m4 * 2] * w,   a3 = A[i + m4 * 3] * w3;
          mod_t t02 = a0 + a2, t13 = a1 + a3;
          A[i + m4 * 0] = t02 + t13; A[i + m4 * 2] = t02 - t13;
          t02 = a0 - a2, t13 = (a1 - a3) * imag;
          A[i + m4 * 1] = t02 + t13; A[i + m4 * 3] = t02 - t13;
        }
        w *= dw; w2 = w * w; w3 = w2 * w;
      }
    }
  }
}

} // namespace ntt

using R = int;
using R64 = i64;

class poly {
public:
#ifdef NTT64
  static const int ntt_threshold = 900; // deg(f * g)
  static const int quotient_threshold = 1800; // deg(f)
  static const int divrem_threshold = 700; // deg(f)
  static const int divrem_pre_threshold = 1600; // deg(f)
#else
  static const int ntt_threshold = 1500; // deg(f * g)
  static const int quotient_threshold = 1500; // deg(f)
  static const int divrem_threshold = 800; // deg(f)
  static const int divrem_pre_threshold = 1600; // deg(f)
#endif

  static R add_mod(R a, R b) { return int(a += b - mod) < 0 ? a + mod : a; }
  static R sub_mod(R a, R b) { return int(a -= b) < 0 ? a + mod : a; }
  static R64 sub_mul_mod(R64 a, R b, R c) {
    i64 t = i64(a) - i64(int(b)) * int(c);
    return t < 0 ? t + lmod : t;
  }
  static R mul_mod(R a, R b) { return R64(a) * b % fast_mod; }
  static R mod_inv(R a) {
    R b = mod, s = 1, t = 0;
    while (b > 0) {
      swap(s -= t * (a / b), t);
      swap(a %= b, b);
    }
    if (a > 1) { fprintf(stderr, "Error: invalid modular inverse\n"); exit(1); };
    return int(s) < 0 ? s + mod : s;
  }
  inline static void vec_add(R64* res, int s, const R* f, R c) {
    rep(i, s) res[i] = sub_mul_mod(res[i], mod - c, f[i]);
  }
  inline static void vec_sub(R64* res, int s, const R* f, R c) {
    rep(i, s) res[i] = sub_mul_mod(res[i], c, f[i]);
  }

#ifdef NTT64
  struct fast_div {
    using u128 = __uint128_t;
    fast_div() {}
    fast_div(u64 n) : m(n) {
      s = (n == 1) ? 0 : 127 - __builtin_clzll(n - 1);
      x = ((u128(1) << s) + n - 1) / n;
    }
    friend u64 operator / (u64 n, fast_div d) { return u128(n) * d.x >> d.s; }
    friend u64 operator % (u64 n, fast_div d) { return n - n / d * d.m; }
    u64 m, s, x;
  };
#else
  struct fast_div {
    fast_div() {}
    fast_div(u32 n) : m(n) {}
    friend u32 operator % (u64 n, fast_div d) { return n % d.m; }
    u32 m;
  };
#endif

public:
  poly() {}
  poly(int n) : coefs(n) {}
  poly(int n, int c) : coefs(n, c % mod) {}
  poly(const R* ar, int s) : coefs(ar, ar + s) {}
  poly(const vector<R>& v) : coefs(v) {}
  poly(const poly& f, int beg, int end=-1) {
    if (end < 0) end = beg, beg = 0;
    resize(end - beg);
    rep(i, beg, end) if (i < f.size()) coefs[i - beg] = f[i];
  }

  static int ilog2(u64 n) {
    return 63 - __builtin_clzll(n);
  }
  int size() const { return coefs.size(); }
  void resize(int s) { coefs.resize(s); }
  void push_back(R c) { coefs.push_back(c); }

  const R* data() const { return coefs.data(); }
  R* data() { return coefs.data(); }
  const R& operator [] (int i) const { return coefs[i]; }
  R& operator [] (int i) { return coefs[i]; }

  void reverse() { std::reverse(coefs.begin(), coefs.end()); }

  poly operator - () {
    poly ret = *this;
    rep(i, ret.size()) ret[i] = (ret[i] == 0 ? 0 : mod - ret[i]);
    return ret;
  }
  poly& operator += (const poly& rhs) {
    if (size() < rhs.size()) resize(rhs.size());
    rep(i, rhs.size()) coefs[i] = add_mod(coefs[i], rhs[i]);
    return *this;
  }
  poly& operator -= (const poly& rhs) {
    if (size() < rhs.size()) resize(rhs.size());
    rep(i, rhs.size()) coefs[i] = sub_mod(coefs[i], rhs[i]);
    return *this;
  }
  poly& operator *= (const poly& rhs) { return *this = *this * rhs; }

  poly& rev_add(const poly& rhs) {
    if (size() < rhs.size()) {
      int s = size();
      resize(rhs.size());
      rep(i, s) coefs[size() - 1 - i] = coefs[s - 1 - i];
      rep(i, size() - s) coefs[i] = 0;
    }
    rep(i, rhs.size()) coefs[size() - 1 - i] = \
      add_mod(coefs[size() - 1 - i], rhs.coefs[rhs.size() - 1 - i]);
    return *this;
  }

  poly operator + (const poly& rhs) const { return poly(*this) += rhs; }
  poly operator - (const poly& rhs) const { return poly(*this) -= rhs; }
  poly operator * (const poly& rhs) const { return this->mul(rhs); }

  static void set_mod(R m, int N=2) {
    mod = m;
    lmod = R64(m) << 32;
    N = max(2, N);
    fast_mod = fast_div(mod);
    invs.assign(N, 1);
    facts.assign(N, 1);
    ifacts.assign(N, 1);
    invs[1] = 1;
    rep(i, 2, N + 1) {
      invs[i] = mul_mod(invs[mod % i], mod - mod / i);
      facts[i] = mul_mod(facts[i - 1], i);
      ifacts[i] = mul_mod(ifacts[i - 1], invs[i]);
    }
  }

private:

#ifdef NTT64
  static poly mul_crt(int beg, int end) {
    using namespace ntt;
    auto inv = m64_2(m64_1::modulus()).inverse();
    auto mod1 = m64_1::modulus() % fast_mod;
    poly ret(end - beg);
    rep(i, ret.size()) {
      u64 r1 = f1[i + beg].get(), r2 = f2[i + beg].get();
      ret[i] = (r1 + (m64_2(r2 + m64_2::modulus() - r1) * inv).get() % fast_mod * mod1) % fast_mod;
    }
    return ret;
  }

  static void mul2(const poly& f, const poly& g, bool cyclic=false) {
    using namespace ntt;
    if (&f == &g) {
      rep(i, f.size()) f1[i] = f[i]; 
      convolve(f1, f.size(), f1, f.size(), cyclic);
      rep(i, f.size()) f2[i] = f[i]; 
      convolve(f2, f.size(), f2, f.size(), cyclic);
    } else {
      rep(i, f.size()) f1[i] = f[i]; rep(i, g.size()) g1[i] = g[i];
      convolve(f1, f.size(), g1, g.size(), cyclic);
      rep(i, f.size()) f2[i] = f[i]; rep(i, g.size()) g2[i] = g[i];
      convolve(f2, f.size(), g2, g.size(), cyclic);
    }
  }
#else
  static poly mul_crt(int beg, int end) {
    using namespace ntt;
    auto m1 = m32_1::modulus();
    auto m2 = m32_2::modulus();
    auto m3 = m32_3::modulus();
    auto m12 = u64(m1) * m2;

    poly ret(end - beg);
    u32 m12m = m12 % mod;
    u32 inv1 = m32_2(m1).inverse().get();
    u32 inv12 = m32_3(m12 % m3).inverse().get();

    rep(i, ret.size()) {
      u32 r1 = f1[i + beg].get(), r2 = f2[i + beg].get(), r3 = f3[i + beg].get();
      u64 r = r1 + u64(r2 + m2 - r1) * inv1 % m2 * m1;
      ret[i] = (r + u64(r3 + m3 - r % m3) * inv12 % m3 * m12m) % mod;
    }
    return ret;
  }

  static void mul2(const poly& f, const poly& g, bool cyclic=false) {
    using namespace ntt;
    if (&f == &g) {
      rep(i, f.size()) f1[i] = f[i] % m32_1::modulus();
      convolve(f1, f.size(), f1, f.size(), cyclic);
      rep(i, f.size()) f2[i] = f[i] % m32_2::modulus();
      convolve(f2, f.size(), f2, f.size(), cyclic);
      rep(i, f.size()) f3[i] = f[i] % m32_3::modulus();
      convolve(f3, f.size(), f3, f.size(), cyclic);
    } else {
      rep(i, f.size()) f1[i] = f[i] % m32_1::modulus(); 
      rep(i, g.size()) g1[i] = g[i] % m32_1::modulus();
      convolve(f1, f.size(), g1, g.size(), cyclic);
      rep(i, f.size()) f2[i] = f[i] % m32_2::modulus(); 
      rep(i, g.size()) g2[i] = g[i] % m32_2::modulus();
      convolve(f2, f.size(), g2, g.size(), cyclic);
      rep(i, f.size()) f3[i] = f[i] % m32_3::modulus(); 
      rep(i, g.size()) g3[i] = g[i] % m32_3::modulus();
      convolve(f3, f.size(), g3, g.size(), cyclic);
    }
  }
#endif 

public:
  static void amul(const R* f, int s1, const R* g, int s2, R* res) {
    int s = s1 + s2 - 1;
    tmp64.assign(s, 0);
    rep(i, s2) if (g[i]) vec_add(tmp64.data() + i, s1, f, g[i]);
    rep(i, s) res[i] = tmp64[i] % fast_mod;
  }

  static void aquotient(const R* f, int s1, const R* g, int s2, R* res) {
    tmp64.resize(s1);
    rep(i, s1) tmp64[i] = f[i];
    rep(i, s1) {
      R c = tmp64[i] % mod;
      if (c) vec_sub(tmp64.data() + i + 1, min(s1 - i, s2) - 1, g + 1, c);
      res[i] = c;
    }
  }

  static void adivrem(const R* f, int s1, const R* g, int s2, R* q, R* r, bool need_r=true) {
    int sq = s1 - s2 + 1;
    tmp64.resize(s1);
    rep(i, s1) tmp64[i] = f[i];
    R inv = mod_inv(g[0]);
    rep(i, sq) {
      R c = tmp64[i] % mod * inv % mod;
      if (c) vec_sub(tmp64.data() + i + 1, s2 - 1, g + 1, c);
      q[i] = c;
    }
    if (need_r) rep(i, sq, s1) r[i - sq] = tmp64[i] % fast_mod;
  }

  poly mul_basecase(const poly& g) const {
    const auto& f = *this;
    int s = size() + g.size() - 1;
    poly ret(s);
    amul(f.data(), f.size(), g.data(), g.size(), ret.data());
    return ret;
  }

  poly quotient_basecase(const poly& g) const {
    const auto& f = *this;
    int s = size();
    poly q(s);
    aquotient(f.data(), f.size(), g.data(), g.size(), q.data());
    return q;
  }

  pair<poly, poly> divrem_basecase(const poly& g) const {
    const auto& f = *this;
    int s1 = f.size(), s2 = g.size();
    int sq = s1 - s2 + 1;
    auto q = poly(sq), r = poly(g.size() - 1);
    adivrem(f.data(), s1, g.data(), s2, q.data(), r.data());
    return make_pair(q, r);
  }

  // 1.0 * M(n)
  poly mul(const poly& g) const {
    const auto& f = *this;
    if (f.size() == 0 || g.size() == 0) return poly();
    if (f.size() + g.size() <= ntt_threshold) {
      return f.mul_basecase(g);
    } else {
      mul2(f, g, false);
      return mul_crt(0, f.size() + g.size() - 1);
    }
  }

  // 0.5 * M(n)
  poly mul_cyclically(const poly& g) const {
    const auto& f = *this;
    if (f.size() == 0 || g.size() == 0) return poly();
    mul2(f, g, true);
    int s = max(f.size(), g.size()), size = 1;
    while (size < s) size <<= 1;
    return mul_crt(0, size);
  }

  // 1.0 * M(n)
  poly middle_product(const poly& g) const {
    const poly& f = *this;
    if (f.size() == 0 || g.size() == 0) return poly();
    mul2(f, g, true);
    return mul_crt(f.size(), g.size());
  }

  // 2.0 * M(n)
  poly inverse(int prec=-1) const {
    if (prec < 0) prec = size();
    poly ret(1, 1);
    for (int e = 1, ne; e < prec; e = ne) {
      ne = min(2 * e, prec);
      poly h = poly(ret, ne - e) * -ret.middle_product(poly(*this, ne));
      rep(i, e, ne) ret.push_back(h[i - e]);
    }
    return ret;
  }

  // 2.5 * M(n)
  poly quotient(const poly& b) const {
    assert(size() == b.size());
    if (b.size() < quotient_threshold) {
      return quotient_basecase(b);
    }
    int s = size() / 2 + 1;
    poly inv = b.inverse(s);
    poly q1 = poly(poly(*this, s) * inv, s);
    poly lo = q1.middle_product(b);
    poly q2 = poly(inv, size() - s) * (poly(*this, s, size()) - lo);
    rep(i, size() - s) q1.push_back(q2[i]);
    return q1;
  }

  // 0.5 * M(n) : f - q * d
  static poly sub_mul(const poly& f, const poly& q, const poly& d) {
    int sq = q.size();
    poly p = q.mul_cyclically(d);
    int mask = p.size() - 1;
    rep(i, sq) p[i & mask] = sub_mod(p[i & mask], f[i & mask]);
    poly r = poly(f, sq, f.size());
    rep(i, r.size()) r[i] = sub_mod(r[i], p[(sq + i) & mask]);
    return r;
  }

  // 3.0 * M(n)
  pair<poly, poly> divrem(const poly& b) const {
    if (size() < b.size()) return make_pair(poly(), poly(*this));
    if (size() < divrem_threshold) {
      return divrem_basecase(b);
    }
    assert(size() < 2 * b.size());
    int sq = size() - b.size() + 1;
    poly q = poly(*this, sq).quotient(poly(b, sq));
    poly r = sub_mul(*this, q, b);
    return make_pair(q, r);
  } 

  // 3.0 * M(n)
  poly rem(const poly& b) const {
    return divrem(b).second;
  }

  // 1.5 * M(n)
  pair<poly, poly> divrem_pre(const poly& b, const poly& inv) const {
    if (size() < b.size()) {
      return make_pair(poly(), poly(*this));
    }
    if (size() < divrem_pre_threshold) {
      return divrem_basecase(b);
    }
    int sq = size() - b.size() + 1;
    assert(size() >= sq && inv.size() >= sq);
    poly q = poly(poly(*this, sq) * poly(inv, sq), sq);
    poly r = sub_mul(*this, q, b);
    return make_pair(q, r);
  }

  // 1.5 * M(n)
  poly rem_pre(const poly& f, const poly& inv) const {
    return divrem_pre(f, inv).second;
  }

  // 2.5 * M(n) : Z/pZ
  poly log() const {
    assert(size() <= int(invs.size()));
    assert(coefs[0] == 1);
    poly ret = poly(*this);
    rep(i, ret.size() - 1) ret[i] = mul_mod(ret[i + 1], i + 1);
    ret = ret.quotient(*this);
    for (int i = ret.size() - 1; i > 0; --i) ret[i] = mul_mod(ret[i - 1], invs[i]);
    ret[0] = 0;
    return ret;
  }

  // 4.0 * M(n) : Z/pZ
  poly exp() const {
    assert(size() <= int(invs.size()));
    assert(coefs[0] == 0);
    poly expf = poly(1, 1);
    poly expfr = poly(1, 1);
    poly df = poly(*this);
    rep(i, df.size() - 1) df[i] = mul_mod(df[i + 1], i + 1);
    for (int e = 1, pe = 1, ne; e < size(); pe = e, e = ne) {
      ne = min(2 * e, size());
      poly tmp = expfr * expfr.middle_product(expf);
      rep(i, e - pe) expfr.push_back((mod - tmp[i]) % fast_mod);
      poly q = expfr * poly(expf * poly(df, e - 1), e - 1, ne - 1);
      tmp.resize(0);
      rep(i, e, ne) tmp.push_back((coefs[i] + mul_mod(q[i - e], invs[i])) % fast_mod);
      tmp = tmp * expf;
      rep(i, ne - e) expf.push_back(tmp[i]);
    }
    return expf;
  }

  // 13/6 * M(n) * log_2(e) : x^e (mod f)
  static poly x_pow_mod(u64 e, const poly& f) {
    if (e == 0) return poly(1, 1);
    poly ret = poly(vector<R>({1, 0}));
    poly inv = f.inverse(f.size());
    ret = ret.rem_pre(f, inv);
    u64 mask = (u64(1) << ilog2(e)) >> 1;
    while (mask) {
      ret *= ret;
      if (e & mask) ret.push_back(0);
      ret = ret.rem_pre(f, inv);
      mask >>= 1;
    }
    return ret;
  }

  // O(n^2) : Z/pZ
  poly mod_inverse(const poly& g) const {
    auto& f = *this;
    assert(f.size() < g.size());

    int s1 = g.size(), s2 = f.size();
    int t1 = 0, t2 = 1;

    tmp32.resize(s1 * 4);
    R* b1 = tmp32.data(), *b2 = b1 + s1;
    R* c1 = b2 + s1, *c2 = c1 + s1;
    c1[0] = 0, c2[0] = 1;

    copy(g.data(), g.data() + s1, b1);
    copy(f.data(), f.data() + s2, b2);

    while (1) {
      while (s2 > 0 && *b2 == 0) --s2, ++b2;
      if (s2 == 0) break;
      int s3 = s2 - 1, sq = s1 - s2 + 1, t3 = s1 - s2 + t2;
      R* b3 = b1 + sq, *c3 = c1;
      adivrem(b1, s1, b2, s2, b1, b3);
      tmp64.assign(t3, 0);
      rep(i, t1) tmp64[t3 - 1 - i] = c1[t1 - 1 - i];
      rep(i, sq) if (b1[i]) vec_sub(tmp64.data() + i, t2, c2, b1[i]);
      rep(i, t3) c3[i] = tmp64[i] % fast_mod;
      b1 = b2; b2 = b3; s1 = s2; s2 = s3;
      c1 = c2; c2 = c3; t1 = t2; t2 = t3;
    }
    if (s1 > 1) {
      fprintf(stderr, "Error: deg(gcd(f, g)) == %d.\n", s1 - 1);
      exit(1);
    }
    if (b1[0] != 1) {
      R inv = mod_inv(b1[0]);
      rep(i, t1) c1[i] = mul_mod(c1[i], inv);
    }
    return poly(c1, t1);
  }

  R evaluate(R x) const {
    R ret = 0;
    rep(i, size()) ret = (u64(ret) * x + coefs[i]) % fast_mod;
    return ret;
  }

  static poly expand(vector<R>& cs) {
    function< poly(int, int) > rec = [&](int beg, int end) {
      if (end - beg == 1) {
        return poly(vector<R>({1, cs[beg] % mod}));
      } 
      int mid = (beg + end) / 2;
      return rec(beg, mid) * rec(mid, end);
    };
    return rec(0, cs.size());
  }

  static vector<R> multipoint_evaluation(const poly& f, vector<R>& points) {
    int s = points.size();
    int tree_size = 4 << ilog2(s - 1);

    vector<poly> tree(tree_size);
    function< void(int, int, int) > rec = [&](int beg, int end, int k) {
      if (end - beg == 1) {
        tree[k] = poly(vector<R>({1, (mod - points[beg] % mod) % mod}));
      } else {
        int mid = (beg + end) >> 1;
        rec(beg, mid, 2 * k + 1);
        rec(mid, end, 2 * k + 2);
        tree[k] = tree[2 * k + 1] * tree[2 * k + 2];
      }
    };
    rec(0, s, 0);

    vector<R> res(s);
    function< void(const poly&, int, int, int) > rec2 = [&](const poly& g, int beg, int end, int k) {
      auto r = g.rem(tree[k]);
      if (end - beg <= 16) {
        rep(i, beg, end) res[i] = r.evaluate(points[i]);
      } else {
        int mid = (beg + end) >> 1;
        rec2(r, beg, mid, 2 * k + 1);
        rec2(r, mid, end, 2 * k + 2);
      }
    };
    rec2(f, 0, s, 0);

    return res;
  }

  static R fact_mod(int N) {
    if (N >= mod) return 0;
    if (N <= 1) return 1 % mod;
    int v = sqrt(N);
    vector<R> cs(v);
    rep(i, v) cs[i] = (i * v + 1);
    auto f = expand(cs);

    rep(i, v) cs[i] = i;
    auto vs = multipoint_evaluation(f, cs);

    R ret = 1;
    rep(i, v) ret = mul_mod(ret, vs[i]);
    rep(i, v * v + 1, N + 1) ret = mul_mod(ret, i);
    return ret;
  }

  void print() const {
    printf("[");
    if (size()) {
      printf("%u", coefs[0]);
      rep(i, 1, size()) printf(", %u", coefs[i]);
    }
    puts("]");
  }

public:
  vector<R> coefs;
  static vector<R> tmp32;
  static vector<R64> tmp64;
  static vector<R> invs, facts, ifacts;
  static R mod;
  static R64 lmod;
  static fast_div fast_mod;
};
R poly::mod;
R64 poly::lmod;
poly::fast_div poly::fast_mod;
vector<R> poly::tmp32;
vector<R64> poly::tmp64;
vector<R> poly::invs, poly::facts, poly::ifacts;

void solve() {
  const u32 mod = 1000000007;
  poly::set_mod(mod);
  i64 N;
  while (~scanf("%lld", &N)) {
    printf("%d\n", poly::fact_mod(min(i64(mod), N)));
  }
}

int main() {
  clock_t beg = clock();
  solve();
  clock_t end = clock();
  fprintf(stderr, "%.3f sec\n", double(end - beg) / CLOCKS_PER_SEC);
  return 0;
}
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