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.

Examples

Input

2 2 100


Output

5


Input

4 3 999999999


Output

358


Input

150 150 998244353


Output

186248260
#include <bits/stdc++.h>
using namespace std;

const int N = 333;

int f[N][N][N], n, K, MOD;

int main(void) {
  scanf("%d%d%d", &n, &K, &MOD);
  f[0][1][0] = 1;
  for(int i = 0; i <= n; i++) {
    for(int j = 1; j <= K; j++) {
      for(int k = i; ~k; k--) {
	if(k) {
	  (f[i][j][k - 1] += f[i][j][k]) %= MOD;
	} else {
	  (f[i][j + 1][i] += f[i][j][k]) %= MOD;
	}
	(f[i + 1][j][k] += 1LL * (k + 1) * f[i][j][k] % MOD) %= MOD;
      }
    }
  }
  cout << f[n][K + 1][n] << endl;
}
