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>

#define For(i, j, k) for (int i = j; i <= k; i++)
#define Forr(i, j, k) for (int i = j; i >= k; i--)

using namespace std;

const int N = 310;

int n, m, Mod;
int C[N][N], dp[N][N], g[N][N], f[N][N];

int main() {

	scanf("%d%d%d", &n, &m, &Mod);
	For(i, 0, n) {
		C[i][0] = 1;
		For(j, 1, i) C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % Mod;
	}

	For(i, 1, m + 1) f[0][i] = 1;
	For(i, 1, n) {
		For(j, 1, m) dp[i][j] = f[i - 1][j + 1];
		Forr(j, m, 1) g[i][j] = (g[i][j + 1] + dp[i][j]) % Mod;
		For(j, 1, m) For(k, 1, i)
			f[i][j] = (f[i][j] + 1ll * g[k][j] * f[i - k][j] % Mod * C[i - 1][k - 1]) % Mod;
	}
	printf("%d\n", f[n][1]);

	return 0;
}