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 f[310][310],n,k,mod,g[310][310],sum[310][310],C[310][310];

int main()
{
	scanf("%d%d%d",&n,&k,&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;
	}
	g[0][k+1]=sum[0][k+1]=1;
	for (int i=k; i; i--)
	{
		for (int j=1; j<=n; j++)
		{
			f[j][i]=0;
			for (int l=i; l<=k+1; l++) 
				f[j][i]=(f[j][i]+g[j-1][l]>=mod?f[j][i]+g[j-1][l]-mod:f[j][i]+g[j-1][l]);
			for (int l=0; l<=n-j; l++)
				g[j+l][i]=(g[j+l][i]+1ll*f[j][i]*sum[l][i+1]%mod*C[j+l][l])%mod;
		}
		for (int j=0; j<=n; j++) sum[j][i]=(sum[j][i+1]+g[j][i])%mod;
	}
	printf("%d\n",sum[n][1]);
	return 0;
}