結果

問題 No.2747 Permutation Adjacent Sum
ユーザー ponjuiceponjuice
提出日時 2024-04-13 18:29:45
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 455 ms / 3,000 ms
コード長 9,581 bytes
コンパイル時間 1,637 ms
コンパイル使用メモリ 111,036 KB
実行使用メモリ 30,720 KB
最終ジャッジ日時 2024-10-03 00:19:36
合計ジャッジ時間 14,433 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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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 269 ms
17,904 KB
testcase_01 AC 168 ms
13,184 KB
testcase_02 AC 224 ms
14,892 KB
testcase_03 AC 171 ms
13,336 KB
testcase_04 AC 278 ms
18,176 KB
testcase_05 AC 455 ms
30,440 KB
testcase_06 AC 291 ms
18,480 KB
testcase_07 AC 263 ms
17,972 KB
testcase_08 AC 338 ms
19,972 KB
testcase_09 AC 413 ms
26,832 KB
testcase_10 AC 187 ms
13,744 KB
testcase_11 AC 266 ms
17,912 KB
testcase_12 AC 162 ms
12,784 KB
testcase_13 AC 205 ms
14,148 KB
testcase_14 AC 316 ms
18,208 KB
testcase_15 AC 405 ms
26,264 KB
testcase_16 AC 271 ms
18,064 KB
testcase_17 AC 390 ms
24,548 KB
testcase_18 AC 377 ms
23,448 KB
testcase_19 AC 176 ms
13,640 KB
testcase_20 AC 279 ms
18,140 KB
testcase_21 AC 344 ms
20,128 KB
testcase_22 AC 356 ms
21,592 KB
testcase_23 AC 249 ms
17,476 KB
testcase_24 AC 255 ms
17,632 KB
testcase_25 AC 220 ms
14,828 KB
testcase_26 AC 319 ms
18,560 KB
testcase_27 AC 346 ms
20,788 KB
testcase_28 AC 339 ms
19,712 KB
testcase_29 AC 279 ms
18,392 KB
testcase_30 AC 297 ms
30,592 KB
testcase_31 AC 298 ms
30,720 KB
testcase_32 AC 294 ms
30,592 KB
testcase_33 AC 301 ms
30,592 KB
testcase_34 AC 297 ms
30,592 KB
testcase_35 AC 162 ms
12,900 KB
testcase_36 AC 162 ms
12,780 KB
testcase_37 AC 162 ms
12,896 KB
testcase_38 AC 163 ms
12,772 KB
testcase_39 AC 163 ms
12,772 KB
testcase_40 AC 160 ms
12,900 KB
testcase_41 AC 166 ms
12,776 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 # 

// O(klogk + √p logp)
#include<iostream>
#include<vector>
#include<cmath>
#include<cassert>
using namespace std;
using ll = long long;

template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(ll 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(ll 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) {
    ll t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }

  ll get(){
    return x;
  }
};

using modint = ModInt<998244353>;

template< typename T >
struct Combination {
  vector< T > _fact, _rfact, _inv;

  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }

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

  inline T rfact(int k) const { return _rfact[k]; }

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

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

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

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

template< typename T >
T lagrange_polynomial(const vector< T > &y, ll t) {
  int N = y.size() - 1;
  Combination< T > comb(N);
  if(t <= N) return y[t];
  T ret(0);
  vector< T > dp(N + 1, 1), pd(N + 1, 1);
  for(int i = 0; i < N; i++) dp[i + 1] = dp[i] * (t - i);
  for(int i = N; i > 0; i--) pd[i - 1] = pd[i] * (t - i);
  for(int i = 0; i <= N; i++) {
    T tmp = y[i] * dp[i] * pd[i] * comb.rfact(i) * comb.rfact(N - i);
    if((N - i) & 1) ret -= tmp;
    else ret += tmp;
  }
  return ret;
}

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< ll > 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< ll > ret(need);
    for(int i = 0; i < need; i++) {
      ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
  }
};

template< typename T >
struct ArbitraryModConvolution {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolution() = default;

  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 < (int)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 < (int)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++) {
      ll aa = llround(fa[i].x);
      ll bb = llround(fb[i].x);
      ll 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;
  }
};

template< typename T >
T factorial(ll n) {
  if(n >= T::get_mod()) return 0;
  ArbitraryModConvolution< T > fft;

  ll d = 1 << 15;
  Combination< T > comb(2 * d);

  vector< T > seq({1, d + 1});
  seq.reserve(d + 1);

  int sz = 1;
  while(sz < d) {
    vector< T > aux(sz, 1), f(sz * 4), g(sz * 4);
    for(int i = 0; i <= sz; i++) {
      f[i] = comb.rfact(i) * comb.rfact(sz - i) * seq[i];
      if(((sz + i) & 1)) f[i] = -f[i];
    }
    vector< T > pf(f), as;
    as.emplace_back(sz + 1);
    as.emplace_back(T(sz) / d);
    as.emplace_back(T(sz) / d + sz + 1);

    for(int idx = 0; idx < 3; idx++) {
      for(int i = 0; i < sz * 4; i++) f[i] = pf[i];
      for(int i = 1; i < sz * 2 + 2; i++) g[i] = T(1) / (as[idx] - sz + i - 1);
      f = fft.multiply(f, g);
      f.resize(sz * 4);
      T prod = 1;
      for(int i = 0; i <= sz; i++) prod *= as[idx] - i;
      for(int i = 0; i <= sz; i++) {
        f[sz + i + 1] *= prod;
        prod *= as[idx] + i + 1;
        prod /= as[idx] - (sz - i);
      }
      if(idx == 0) {
        for(int i = 0; i < sz; i++) aux[i] = f[sz + i + 1];
      } else if(idx == 1) {
        for(int i = 0; i <= sz; i++) seq[i] *= f[sz + i + 1];
      } else {
        for(int i = 0; i < sz; i++) aux[i] *= f[sz + i + 1];
      }
    }
    for(auto x : aux) seq.emplace_back(x);
    sz <<= 1;
  }

  T res = 1;
  ll l = min(d, (n + 1) / d);
  for(ll i = 0; i < l; i++) res *= seq[i];
  for(ll i = l * d + 1; i <= n; i++) res *= i;
  return res;
}


int main(){
    ll n,k;
    cin >> n >> k;

    ll siz = k + 3;
    vector<modint> k1(siz,0 ), k2(siz, 0);
    for(int i = 1; i < siz; i++) {
        k1[i] = modint(i).pow(k) + k1[i-1];
        k2[i] = modint(i).pow(k+1) + k2[i-1];
    }

    cout << factorial<modint>(n-1) * 2 * (lagrange_polynomial(k1, n) * n - lagrange_polynomial(k2, n)) << endl;
}
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