結果

問題 No.2164 Equal Balls
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-12-15 00:14:21
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,052 ms / 5,000 ms
コード長 10,676 bytes
コンパイル時間 1,562 ms
コンパイル使用メモリ 113,640 KB
実行使用メモリ 21,788 KB
最終ジャッジ日時 2024-11-08 16:42:10
合計ジャッジ時間 26,919 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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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 9 ms
8,320 KB
testcase_01 AC 10 ms
8,320 KB
testcase_02 AC 10 ms
8,320 KB
testcase_03 AC 10 ms
8,320 KB
testcase_04 AC 10 ms
8,320 KB
testcase_05 AC 10 ms
8,320 KB
testcase_06 AC 10 ms
8,448 KB
testcase_07 AC 10 ms
8,320 KB
testcase_08 AC 59 ms
12,436 KB
testcase_09 AC 46 ms
11,264 KB
testcase_10 AC 30 ms
9,892 KB
testcase_11 AC 102 ms
15,960 KB
testcase_12 AC 63 ms
12,604 KB
testcase_13 AC 40 ms
10,752 KB
testcase_14 AC 51 ms
11,512 KB
testcase_15 AC 98 ms
15,640 KB
testcase_16 AC 56 ms
12,264 KB
testcase_17 AC 20 ms
9,088 KB
testcase_18 AC 75 ms
13,908 KB
testcase_19 AC 122 ms
17,552 KB
testcase_20 AC 66 ms
12,928 KB
testcase_21 AC 17 ms
8,776 KB
testcase_22 AC 17 ms
8,632 KB
testcase_23 AC 505 ms
11,264 KB
testcase_24 AC 358 ms
18,804 KB
testcase_25 AC 450 ms
9,600 KB
testcase_26 AC 202 ms
19,264 KB
testcase_27 AC 425 ms
20,660 KB
testcase_28 AC 432 ms
20,440 KB
testcase_29 AC 184 ms
11,008 KB
testcase_30 AC 393 ms
16,516 KB
testcase_31 AC 620 ms
10,752 KB
testcase_32 AC 458 ms
19,408 KB
testcase_33 AC 320 ms
9,856 KB
testcase_34 AC 426 ms
11,648 KB
testcase_35 AC 92 ms
8,576 KB
testcase_36 AC 832 ms
20,492 KB
testcase_37 AC 721 ms
10,368 KB
testcase_38 AC 1,052 ms
21,784 KB
testcase_39 AC 1,040 ms
21,788 KB
testcase_40 AC 1,045 ms
21,784 KB
testcase_41 AC 1,047 ms
21,660 KB
testcase_42 AC 1,048 ms
21,788 KB
testcase_43 AC 1,041 ms
21,664 KB
testcase_44 AC 1,042 ms
21,784 KB
testcase_45 AC 1,039 ms
21,784 KB
testcase_46 AC 1,037 ms
21,784 KB
testcase_47 AC 1,046 ms
21,660 KB
testcase_48 AC 1,043 ms
21,656 KB
testcase_49 AC 892 ms
9,728 KB
testcase_50 AC 902 ms
9,600 KB
testcase_51 AC 899 ms
9,600 KB
testcase_52 AC 899 ms
9,600 KB
testcase_53 AC 896 ms
9,600 KB
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ソースコード

diff # 

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};

// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = n;
  if (m >>= 1) {
    for (int i = 0; i < m; ++i) {
      const unsigned x = as[i + m].x;  // < MO
      as[i + m].x = as[i].x + MO - x;  // < 2 MO
      as[i].x += x;  // < 2 MO
    }
  }
  if (m >>= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned x = (prod * as[i + m]).x;  // < MO
        as[i + m].x = as[i].x + MO - x;  // < 3 MO
        as[i].x += x;  // < 3 MO
      }
      prod *= FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  for (; m; ) {
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i + m].x = as[i].x + MO - x;  // < 4 MO
          as[i].x += x;  // < 4 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
          as[i + m].x = as[i].x + MO - x;  // < 3 MO
          as[i].x += x;  // < 3 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
    as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x;  // < MO
  }
}

// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = 1;
  if (m < n >> 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
    m <<= 1;
  }
  for (; m < n >> 1; m <<= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + (m >> 1); ++i) {
        const unsigned long long y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
        as[i].x += as[i + m].x;  // < 4 MO
        as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  if (m < n) {
    for (int i = 0; i < m; ++i) {
      const unsigned y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
      as[i].x += as[i + m].x;  // < 4 MO
      as[i + m].x = y;  // < 4 MO
    }
  }
  const Mint invN = Mint(n).inv();
  for (int i = 0; i < n; ++i) {
    as[i] *= invN;
  }
}

void fft(vector<Mint> &as) {
  fft(as.data(), as.size());
}
void invFft(vector<Mint> &as) {
  invFft(as.data(), as.size());
}

vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {
  if (as.empty() || bs.empty()) return {};
  const int len = as.size() + bs.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  bs.resize(n); fft(bs);
  for (int i = 0; i < n; ++i) as[i] *= bs[i];
  invFft(as);
  as.resize(len);
  return as;
}
vector<Mint> square(vector<Mint> as) {
  if (as.empty()) return {};
  const int len = as.size() + as.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  for (int i = 0; i < n; ++i) as[i] *= as[i];
  invFft(as);
  as.resize(len);
  return as;
}
////////////////////////////////////////////////////////////////////////////////


constexpr int LIM_INV = 400'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


int N, M;
vector<int> A, B;

int main() {
  prepare();
  
  for (; ~scanf("%d%d", &N, &M); ) {
    A.resize(N); for (int i = 0; i < N; ++i) scanf("%d", &A[i]);
    B.resize(N); for (int i = 0; i < N; ++i) scanf("%d", &B[i]);
    
    int lim = 0;
    chmax(lim, *max_element(A.begin(), A.end()));
    chmax(lim, *max_element(B.begin(), B.end()));
    vector<vector<Mint>> fss(2 * M - 1);
    for (int j = 0; j < M; ++j) {
      fss[j].assign(2 * lim + 1, 1);
      for (int i = j; i < N; i += M) {
        for (int k = -lim; k <= +lim; ++k) {
          fss[j][lim + k] *= binom(A[i] + B[i], k + B[i]);
        }
      }
    }
    for (int j = 0; j < M - 1; ++j) {
      fss[M + j] = convolve(fss[j << 1], fss[j << 1 | 1]);
    }
    const Mint ans = fss.back()[M * lim];
    printf("%u\n", ans.x);
  }
  return 0;
}
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