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;

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

int main () {
	int n, k, mod; scanf("%d%d%d", &n, &k, &mod);
	for (int i = 0; i <= 300; i++) {
		C[i][0] = 1;
		for (int j = 1; j <= i; j++) {
			C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
		}
	}
	for (int i = 0; i <= k; i++) {
		dp[1][i] = 1;
	}
	for (int i = 2; i <= n + 1; i++) {
		for (int j = k; j >= 0; j--) {
			sum[i - 1][j] = (sum[i - 1][j + 1] + dp[i - 1][j]) % mod;
		}
		for (int j = 0; j <= k; j++) {
			for (int ni = 1; ni <= i - 1; ni++) {
				dp[i][j] = (dp[i][j] + sum[ni][j + 1] * C[i - 2][ni - 1] % mod * dp[i - ni][j]) % mod;
			}
		}
	}
	printf("%lld\n", dp[n + 1][0]);
	return 0;
}
