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; 
ll dp[305][305], C[305][305], pre[305][305]; 
int main()
{
	// freopen("AGC024-E.in", "r", stdin); 
	int n, lim, mod; 
	scanf("%d%d%d", &n, &lim, &mod);
	for (int i = 0; i <= n; i++)
	{
		C[i][0] = 1; 
		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 <= lim; i++)
	{
		dp[1][i] = 1; 
		pre[1][i] = lim - i + 1; 
	}
	for (int i = 2; i <= n + 1; i++)
	{
		for (int j = lim; j >= 0; j--)
		{
			for (int k = 1; k < i; k++)
				(dp[i][j] += C[i - 2][k - 1] * dp[i - k][j] % mod * pre[k][j + 1]) %= mod; 
			pre[i][j] = (pre[i][j + 1] + dp[i][j]) % mod; 
		}
	}
	printf("%lld\n", dp[n + 1][0]);
	return 0; 
}
