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>
#include <iostream>

using namespace std;

int n , m , mod;

const int N = 305;

int f[N][N][N];

#define add(x , y) x = (x + y >= mod ? x + y - mod : x + y)

int main() {
	cin >> n >> m >> mod;
	f[0][1][0] = 1;
	for (int i = 0; i <= n; i++)
		for (int j = 1; j <= m; j++)
			for (int k = i; k >= 0; k--) {
				if (k) 
					add(f[i][j][k - 1] , f[i][j][k]);
				else 
					add(f[i][j + 1][i] , f[i][j][k]);
				add(f[i + 1][j][k] , 1ll * f[i][j][k] * (k + 1) % mod);
	}
	cout << f[n][m][0];
	return 0;
}