結果

問題 No.2097 AND^k
ユーザー chro_96chro_96
提出日時 2023-03-07 01:06:39
言語 C
(gcc 12.3.0)
結果
AC  
実行時間 4,212 ms / 5,000 ms
コード長 5,141 bytes
コンパイル時間 607 ms
コンパイル使用メモリ 34,236 KB
実行使用メモリ 10,476 KB
最終ジャッジ日時 2024-09-18 02:00:37
合計ジャッジ時間 52,986 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 3 ms
10,348 KB
testcase_01 AC 3 ms
10,400 KB
testcase_02 AC 3 ms
10,344 KB
testcase_03 AC 4 ms
10,300 KB
testcase_04 AC 4 ms
10,344 KB
testcase_05 AC 4 ms
10,476 KB
testcase_06 AC 5 ms
10,424 KB
testcase_07 AC 4 ms
10,348 KB
testcase_08 AC 3,247 ms
10,476 KB
testcase_09 AC 663 ms
10,344 KB
testcase_10 AC 3,509 ms
10,348 KB
testcase_11 AC 624 ms
10,348 KB
testcase_12 AC 555 ms
10,344 KB
testcase_13 AC 3,509 ms
10,472 KB
testcase_14 AC 3,399 ms
10,472 KB
testcase_15 AC 4,121 ms
10,472 KB
testcase_16 AC 3,366 ms
10,472 KB
testcase_17 AC 3,742 ms
10,348 KB
testcase_18 AC 3,566 ms
10,472 KB
testcase_19 AC 3,218 ms
10,348 KB
testcase_20 AC 3,199 ms
10,348 KB
testcase_21 AC 3,234 ms
10,284 KB
testcase_22 AC 3,345 ms
10,316 KB
testcase_23 AC 3,306 ms
10,468 KB
testcase_24 AC 4 ms
10,448 KB
testcase_25 AC 4,212 ms
10,348 KB
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ソースコード

diff # 

#include <stdio.h>

long long mod_num = 998244353LL;
long long root = 3LL;
int length = 998244352;
long long inverse_root = 0LL;
long long inverse_l = 0LL;

int log_l = 0;
long long pow_root[16] = {};
long long pow_root_inv[16] = {};

long long power_mod (long long a, long long b, long long p) {
  long long ans = 0LL;
  
  a %= p;
  
  if (b <= 0LL) {
    return 1LL;
  }
  
  ans = power_mod(a, b/2LL, p);
  ans = (ans * ans) % p;
  if (b%2LL == 1LL) {
    ans = (ans * a) % p;
  }
  
  return ans;
}

void setup_ntt (int l) {
  int tmp_length = 4;
  log_l = 1;
  
  while(tmp_length < 2*l) {
    tmp_length *= 4;
    log_l++;
  }
  
  root = power_mod(root, length / tmp_length, mod_num);
  inverse_root = power_mod(root, mod_num-2LL, mod_num);
  inverse_l = power_mod((long long) tmp_length, mod_num-2LL, mod_num);
  length = tmp_length;
  
  pow_root[log_l-1] = root;
  for (int i = log_l-1; i > 0; i--) {
    pow_root[i-1] = pow_root[i];
    pow_root[i-1] *= pow_root[i];
    pow_root[i-1] %= mod_num;
    pow_root[i-1] *= pow_root[i-1];
    pow_root[i-1] %= mod_num;
  }
  
  pow_root_inv[log_l-1] = inverse_root;
  for (int i = log_l-1; i > 0; i--) {
    pow_root_inv[i-1] = pow_root_inv[i];
    pow_root_inv[i-1] *= pow_root_inv[i];
    pow_root_inv[i-1] %= mod_num;
    pow_root_inv[i-1] *= pow_root_inv[i-1];
    pow_root_inv[i-1] %= mod_num;
  }
  
  return;
}

void ntt_4n (long long *a, long long *pow_root) {
  long long root_1_4 = pow_root[0];
  
  for (int i = 0; i < length; i++) {
    int idx = 0;
    int tmp = i;
    for (int j = 0; j < log_l; j++) {
      idx <<= 2;
      idx |= (tmp&3);
      tmp >>= 2;
    }
    if (i < idx) {
      long long swap = a[i];
      a[i] = a[idx];
      a[idx] = swap;
    }
  }
  
  for (int i = 0; i < log_l; i++) {
    int ix2 = 2*i;
    int ix2_2 = ix2+2;
    int step = (1<<ix2);
    int cnt = length>>ix2_2;
    long long tmp_root = 1LL;
    for (int j = 0; j < step; j++) {
      long long w1 = tmp_root;
      long long w2 = (w1*w1)%mod_num;
      long long w3 = (w2*w1)%mod_num;
      for (int k = 0; k < cnt; k++) {
        int idx1 = ((k<<ix2_2)|j);
        int idx2 = (idx1|step);
        int idx3 = (idx1|(2<<ix2));
        int idx4 = (idx2|idx3);
        long long a1 = a[idx1]%mod_num;
        long long a2 = (a[idx2]*w1)%mod_num;
        long long a3 = (a[idx3]*w2)%mod_num;
        long long a4 = (a[idx4]*w3)%mod_num;
        long long wa2 = (a2*root_1_4)%mod_num;
        long long wa4 = (a4*root_1_4)%mod_num;
        long long pad = (mod_num<<1LL);
        a[idx1] = a1+a2+a3+a4;
        a[idx2] = a1+wa2-a3-wa4+pad;
        a[idx3] = a1-a2+a3-a4+pad;
        a[idx4] = a1-wa2-a3+wa4+pad;
      }
      tmp_root = (tmp_root*pow_root[i])%mod_num;
    }
  }
  
  for (int i = 0; i < length; i++) {
    a[i] %= mod_num;
  }
  
  return;
}

int main () {
  int n = 0;
  int m = 0;
  int l = 0;
  
  int res = 0;
  
  long long ans[300000] = {};
  long long work[2][300000] = {};
  
  long long pow2 = 2LL;
  long long fact[100001] = {};
  long long invf[100001] = {};
  
  long long inv_cnt = 0LL;
  long long pow_cnt = 0LL;
  long long pow_inv_l = 0LL;
  
  res = scanf("%d", &n);
  res = scanf("%d", &m);
  res = scanf("%d", &l);
  
  fact[0] = 1LL;
  for (int i = 0; i < l; i++) {
    fact[i+1] = fact[i];
    fact[i+1] *= (long long) (i+1);
    fact[i+1] %= mod_num;
  }
  
  invf[l] = power_mod(fact[l], mod_num-2LL, mod_num);
  for (int i = l; i > 0; i--) {
    invf[i-1] = invf[i];
    invf[i-1] *= (long long)i;
    invf[i-1] %= mod_num;
  }
  
  setup_ntt(l+1);
  
  work[0][0] = power_mod(2LL, (long long)n, mod_num);
  for (int i = 1; i <= l; i++) {
    work[0][i] = invf[i];
  }
  
  for (int i = 0; i <= l; i++) {
    work[1][i] = work[0][i];
  }
  ntt_4n(work[1], pow_root);
  
  if (m%2 == 1) {
    for (int i = 0; i <= l; i++) {
      ans[i] = work[0][i];
    }
  } else {
    ans[0] = 1LL;
  }
  
  m /= 2;
  
  while (m > 0) {
    long long p = 1LL;
    for (int j = 0; j <= l; j++) {
      work[0][j] *= p;
      work[0][j] %= mod_num;
      p = (p*pow2)%mod_num;
    }
    ntt_4n(work[0], pow_root);
    for (int j = 0; j < length; j++) {
      work[0][j] *= work[1][j];
      work[0][j] %= mod_num;
    }
    ntt_4n(work[0], pow_root_inv);
    for (int j = 0; j <= l; j++) {
      work[1][j] = work[0][j];
    }
    for (int j = l+1; j < length; j++) {
      work[0][j] = 0LL;
      work[1][j] = 0LL;
    }
    pow_cnt = 2LL*pow_cnt+1LL;
    ntt_4n(work[1], pow_root);
    pow2 = (pow2*pow2)%mod_num;
    if (m%2 == 1) {
      long long p = 1LL;
      for (int i = 0; i <= l; i++) {
        ans[i] *= p;
        ans[i] %= mod_num;
        p = (p*pow2)%mod_num;
      }
      for (int i = l+1; i < length; i++) {
        ans[i] = 0LL;
      }
      ntt_4n(ans, pow_root);
      for (int i = 0; i < length; i++) {
        ans[i] *= work[1][i];
        ans[i] %= mod_num;
      }
      ntt_4n(ans, pow_root_inv);
      inv_cnt += pow_cnt+1LL;
    }
    m /= 2;
  }
  
  pow_inv_l = power_mod(inverse_l, inv_cnt, mod_num);
  for (int i = 0; i < l; i++) {
    printf("%lld\n", (((ans[i+1]*pow_inv_l)%mod_num)*fact[i+1])%mod_num);
  }
  
  return 0;
}
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