Problem:


Score : 1200 points

Problem Statement

Find the number of the possible tuples of sequences (A_0,A_1,...,A_N) that satisfy all of the following conditions, modulo M:

For every i (0\leq i\leq N), A_i is a sequence of length i consisting of integers between 1 and K (inclusive);

For every i (1\leq i\leq N), A_{i-1} is a subsequence of A_i, that is, there exists 1\leq x_i\leq i such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};

For every i (1\leq i\leq N), A_i is lexicographically larger than A_{i-1}.

Constraints

1 \leq N,K \leq 300

2 \leq M \leq 10^9

N, K and M are integers.

Input

Input is given from Standard Input in the following format:

N K M

Output

Print the number of the possible tuples of sequences (A_0,A_1,...,A_N), modulo M.

Sample Input 1

2 2 100

Sample Output 1

5

Five tuples below satisfy the conditions:

(),(1),(1,1)

(),(1),(1,2)

(),(1),(2,1)

(),(2),(2,1)

(),(2),(2,2)

Sample Input 2

4 3 999999999

Sample Output 2

358

Sample Input 3

150 150 998244353

Sample Output 3

186248260



Sample input:
2 2 100


Sample output:
5

Submission status: Runtime Error

Solution code:
#include <bits/stdc++.h>

using namespace std;

vector< vector< int64_t > > get_combination(int N, int M) {
  vector< vector< int64_t > > mat(N + 1, vector< int64_t >(N + 1));
  for(int i = 0; i <= N; i++) {
    for(int j = 0; j <= i; j++) {
      if(j == 0 || j == i) mat[i][j] = 1;
      else mat[i][j] = mat[i - 1][j - 1] + mat[i - 1][j];
      mat[i][j] %= M;
    }
  }
  return (mat);
}

int main() {
  int N, K, M;
  cin >> N >> K >> M;
  auto C = get_combination(N, M);
  int dp[302][302] = {{}};
  for(int i = 0; i <= K; i++) {
    dp[1][i] = 1;
  }
  for(int i = 2; i <= N + 1; i++) {
    int sub[302] = {};
    for(int j = K - 1; j >= 0; j--) {
      for(int k = 0; k < i; k++) {
        sub[k] += dp[k][j + 1];
        sub[k] %= M;
      }
      for(int k = 1; k <= i; k++) {
        dp[i][j] += 1LL * dp[i - k][j] * C[i - 2][k - 1] % M * sub[k] % M;
        dp[i][j] %= M;
      }
    }
  }
  cout << dp[N + 1][0] << endl;
}