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;
#define ll long long
const int N=305;
int binom[N][N];
int dp[N][N],sum[N][N];
int main()
{
	int n,k,m,i,j,l;
	scanf("%i %i %i",&n,&k,&m);
	for(i=0;i<=n+1;i++)
	{
		binom[i][0]=1;
		if(i>0) for(j=1;j<=n+1;j++) binom[i][j]=(binom[i-1][j-1]+binom[i-1][j])%m;
	}
	for(i=1;i<=n+1;i++)
	{
		for(j=k;j>=0;j--)
		{
			if(i==1) dp[i][j]=1;
			else
			{
				for(l=1;l<i;l++)
				{
					int pre=sum[l][k]-sum[l][j];
					if(pre<0) pre+=m;
					int comb=binom[i-2][l-1];
					dp[i][j]+=(ll)comb*pre%m*dp[i-l][j]%m;
					if(dp[i][j]>=m) dp[i][j]-=m;
				}
			}
		}
		for(j=1;j<=k;j++) sum[i][j]=(sum[i][j-1]+dp[i][j])%m;
	}
	printf("%i\n",dp[n+1][0]);
	return 0;
}