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;

#define LL long long

const int maxN = 305;

int n, m;
LL mod;
LL C[maxN + 1][maxN + 1], f[maxN + 1][maxN + 1], sum[maxN + 1][maxN + 1];

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