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>
#define Maxn 307
using namespace std;
int N,m,modp;
int c[Maxn][Maxn],f[Maxn][Maxn],s[Maxn][Maxn];
int main()
{
	scanf("%d%d%d",&N,&m,&modp);
	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]+c[i-1][j-1])%modp;
	}
	for (int i=0;i<=m;i++)
		f[0][i]=1,s[0][i]=i+1;
	for (int n=1;n<=N;n++)
		for (int k=1;k<=m;k++)
		{
			f[n][k]=0;
			for (int j=0;j<n;j++)
			{
				int del=(1LL*c[n-1][j]*f[n-j-1][k])%modp;
				del=(1LL*del*s[j][k-1])%modp;
				f[n][k]=(f[n][k]+del)%modp;
			}
			s[n][k]=(s[n][k-1]+f[n][k])%modp;
		}
	printf("%d\n",f[N][m]);
	return 0;
}
