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;

int dp[310][310], sum[310];
int C[310][310];

int main () {
	int n, k, mod; cin >> n >> k >> mod;
	C[0][0] = 1;
	for (int i = 1; i <= n + 1; i++) {
		for (int j = 0; j <= i; j++) {
			C[i][j] = (C[i - 1][j] + (j ? C[i - 1][j - 1] : 0)) % mod;
		}
	}
	for (int i = 0; i <= k; i++) {
		dp[1][i] = 1;
	}
	for (int i = 2; i <= n + 1; i++) {
		memset(sum, 0, sizeof(sum));
		for (int j = k - 1; j >= 0; j--) {
			for (int t = 1; t < i; t++) {
				(sum[t] += dp[t][j + 1]) %= mod;
			}
			for (int t = 1; t < i; t++) {
				(dp[i][j] += 1ll * dp[i - t][j] * sum[t] % mod * C[i - 2][t - 1] % mod) %= mod;
			}
		}
	}
	printf("%d\n", dp[n + 1][0]);
	return 0;
}
