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<cstdio>
int n, K, Mod, D[310][310], Comb[310][310], S[310];
int main() {
	int i, j, k;
	scanf("%d%d%d", &n, &K, &Mod);
	for (i = 0; i < 310; i++) {
		Comb[i][0] = 1;
		for (j = 1; j <= i; j++)Comb[i][j] = (Comb[i - 1][j - 1] + Comb[i - 1][j]) % Mod;
	}
	D[0][0] = 1;
	for (i = 1; i <= 300; i++) {
		for (j = 0; j <= 300; j++) {
			S[j] = (S[j] + D[i - 1][j]) % Mod;
		}
		D[i][0] = 1;
		for (j = 1; j <= 300; j++) {
			for (k = 1; k <= j; k++) {
				D[i][j] = (D[i][j] + (long long)S[k - 1] * D[i][j - k] % Mod * Comb[j - 1][k - 1]) % Mod;
			}
		}
	}
	printf("%d\n", D[K][n]);
}