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;

int n,k,m;
int dp[305][305];
int sum[305][305];
int C[305][305];

int main()
{
	scanf("%d%d%d",&n,&k,&m);
	for(int i = 0;i <= k; ++ i) dp[1][i] = 1,sum[1][i] = k - i + 1;
	C[0][0] = 1;
	for(int i = 1;i <= 300; ++ i)
	{
		C[i][0] = 1;
		for(int j = 1;j <= i; ++ j)
			C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % m;
	}
	for(int i = 2;i <= n + 1; ++ i)
		for(int j = k - 1;j >= 0; -- j)
		{
			for(int l = 1;l < i; ++ l)
				dp[i][j] = (dp[i][j] + dp[l][j] * 1ll * sum[i - l][j + 1] % m * C[i - 2][l - 1] % m) % m;
			sum[i][j] = sum[i][j + 1] + dp[i][j],sum[i][j] %= m;
		}
	printf("%d\n",dp[n + 1][0]);
}