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 = 320;

int f[N][N], g[N][N], n, m, mod, C[N][N];

int main() {
  scanf("%d%d%d", &n, &m, &mod);
  for (int i = 0; i < N; i ++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j ++)
      C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
  }
  for (int i = 0; i <= m; i ++)
    f[1][i] = 1, g[1][i] = m - i + 1;
  for (int i = 2; i <= n + 1; i ++) {
    for (int k = 0; k <= m; k ++) {
      long long tot = 0;
      for (int j = 1; j < i; j ++)
        tot += 1ll * f[i - j][k] * g[j][k + 1] % mod * C[i - 2][j - 1] % mod;
      f[i][k] = tot % mod;
    }
    for (int k = m; k >= 0; k --)
      g[i][k] = (g[i][k + 1] + f[i][k]) % mod;
  }
  printf("%d\n", f[n + 1][0]);
  return 0;
}