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>

typedef long long LL;

const int MN = 305, MK = 305;

int N, K, Mod;
int C[MN][MK], f[MN][MK];

int main() {
	scanf("%d%d%d", &N, &K, &Mod);
	for (int i = 0; i <= N; ++i) C[i][0] = 1;
	for (int i = 1; i <= N; ++i)
		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 <= K; ++i) f[1][i] = 1;
	for (int i = 2; i <= N + 1; ++i) {
		for (int k = 1; k < i; ++k) {
			int Sum = 0;
			for (int j = K; j >= 0; --j) {
				f[i][j] = (f[i][j] + (LL)f[i - k][j] * Sum % Mod * C[i - 2][k - 1]) % Mod;
				Sum = (Sum + f[k][j]) % Mod;
			}
		}
	}
	printf("%d\n", f[N + 1][0]);
	return 0;
}