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;
const int N=305;
#define int long long
int n,k,p,f[305][305][305];
signed main()
{
	f[0][1][0]=1;
	scanf("%d%d%d",&n,&k,&p);
	for (int i=0;i<=n;i++)
	 for (int j=1;j<=k;j++)
	  for (int l=i;l>=0;l--)
	   if (f[i][j][l]) 
	   	{
	   		if (l)(f[i][j][l-1]+=f[i][j][l])%=p;
	   		else (f[i][j+1][i]+=f[i][j][l])%=p;
	   		(f[i+1][j][l]+=f[i][j][l]*(l+1))%=p;
	    }
	printf("%d",f[n][k+1][n]);   
}