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 = 302;
int n, k, mod, c[N][N], f[N][N], g[N][N];

int main() {
  scanf("%d%d%d", &n, &k, &mod);
  c[0][0] = 1;
  for (int i = 1; i <= n + 1; 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 j = 1; j <= k + 1; j++) {
    f[1][j] = 1;
    g[1][j] = j;
  }
  for (int i = 2; i <= n + 1; i++) {
    for (int j = 1; j <= k + 1; j++) {
      for (int l = 1; l <= i - 1; l++) {
        f[i][j] = (f[i][j] + (long long) g[l][j - 1] * f[i - l][j] % mod * c[i - 2][l - 1]) % mod;
      }
      g[i][j] = (g[i][j - 1] + f[i][j]) % mod;
    }
  }
  printf("%d\n", f[n + 1][k + 1]);
}
