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>
long long dp[305][305][305], MOD;
int main()
{
	// freopen("AGC024-E.in", "r", stdin); 
	int n, k;
	scanf("%d%d%lld", &n, &k, &MOD); 
	dp[0][0][0] = 1; 
	for (int i = 0; i <= n; i++)
	{
		for (int j = 0; j < k; j++)
		{
			for (int x = i; x >= 0; x--)
			{
				if (x)
					(dp[i][j][x - 1] += dp[i][j][x]) %= MOD; 
				else
					(dp[i][j + 1][i] += dp[i][j][x]) %= MOD;
				(dp[i + 1][j][x] += dp[i][j][x] * (x + 1)) %= MOD; 
			}
		}
	}
	printf("%lld\n", dp[n][k][n]);
	return 0; 
}
