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<stdio.h>
typedef long long ll;
ll dp[311][311][311];
int main()
{
	int num, gen;
	ll mod;
	scanf("%d%d%lld", &num, &gen, &mod);
	dp[0][0][0] = 1;
	for (int i = 0; i < gen; i++)
	{
		for (int j = 0; j <= num; j++)dp[i + 1][j][j] = dp[i][j][0];
		for (int j = 0; j <= num; j++)for (int k = j - 1; k >= 0; k--)dp[i + 1][j][k] = (dp[i + 1][j][k + 1] + dp[i + 1][j - 1][k] * (k + 1)) % mod;
	}
	printf("%lld\n", dp[gen][num][0]);
}
