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  1. #include <iostream>
  2.  
  3. using namespace std;
  4.  
  5. const int MAXN = 705;
  6. long long nCr[MAXN][MAXN];
  7. long long S[MAXN][MAXN];
  8. long long power2[MAXN];
  9. long long C_arr[MAXN][MAXN];
  10. long long p_powers[MAXN];
  11. long long E[MAXN];
  12.  
  13. int main() {
  14.     ios_base::sync_with_stdio(false);
  15.     cin.tie(NULL);
  16.  
  17.     int N;
  18.     long long P;
  19.     if (!(cin >> N >> P)) return 0;
  20.  
  21.     for (int i = 0; i <= N; ++i) {
  22.         nCr[i][0] = 1;
  23.         for (int j = 1; j <= i; ++j) {
  24.             nCr[i][j] = nCr[i - 1][j - 1] + nCr[i - 1][j];
  25.             if (nCr[i][j] >= P) nCr[i][j] -= P;
  26.         }
  27.     }
  28.  
  29.     S[0][0] = 1;
  30.     for (int i = 1; i <= N; ++i) {
  31.         for (int j = 1; j <= i; ++j) {
  32.             S[i][j] = (S[i - 1][j - 1] + j * S[i - 1][j]) % P;
  33.         }
  34.     }
  35.  
  36.     power2[0] = 1;
  37.     for (int i = 1; i <= N; ++i) {
  38.         power2[i] = (power2[i - 1] * 2);
  39.         if (power2[i] >= P) power2[i] -= P;
  40.     }
  41.  
  42.     for (int k = 0; k <= N; ++k) {
  43.         long long x = power2[k];
  44.         p_powers[0] = 1;
  45.         for (int j = 1; j <= N; ++j) {
  46.             p_powers[j] = (p_powers[j - 1] * x) % P;
  47.         }
  48.         for (int s = 1; s <= N; ++s) {
  49.             long long sum = 0;
  50.             for (int j = 1; j <= s; ++j) {
  51.                 long long term = (S[s][j] * p_powers[j]) % P;
  52.                 if (j & 1) {
  53.                     sum += term;
  54.                     if (sum >= P) sum -= P;
  55.                 } else {
  56.                     sum -= term;
  57.                     if (sum < 0) sum += P;
  58.                 }
  59.             }
  60.             C_arr[s][k] = sum;
  61.         }
  62.     }
  63.  
  64.     E[0] = 1;
  65.     for (int m = 1; m <= N; ++m) {
  66.         long long sum = 0;
  67.         for (int s = 1; s <= m; ++s) {
  68.             long long ways = C_arr[s][m - s];
  69.             long long term = (ways * E[m - s]) % P;
  70.             term = (term * nCr[m][s]) % P;
  71.             sum += term;
  72.             if (sum >= P) sum -= P;
  73.         }
  74.         E[m] = sum;
  75.     }
  76.  
  77.     long long ans = 0;
  78.     for (int m = 0; m <= N; ++m) {
  79.         long long term = (nCr[N][m] * E[m]) % P;
  80.         ans += term;
  81.         if (ans >= P) ans -= P;
  82.     }
  83.  
  84.     cout << ans << "\n";
  85.  
  86.     return 0;
  87. }
Success #stdin #stdout 0.01s 10044KB
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stdin
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77 777777773
stdout
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381787647
https://ideone.com/p4pgma
language:
C++14 (gcc 8.3)
created:
8 hours ago
visibility:
public

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