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 dp[305][305];
int s[305][305];
int c[305][305];
int n,k,mod;
inline int add(int a,int b)
{return (a+b>=mod?a+b-mod:a+b);}
int main (){
	int i,j,l;
	scanf ("%d%d%d",&n,&k,&mod);
	for (i=0;i<=k;i++) dp[1][i]=1;
	for (i=0;i<=k;i++) s[1][i]=(k-i+1)%mod;
	for (i=0;i<=n+1;i++)
	{c[i][0]=c[i][i]=1;
	for (j=1;j<i;j++)
	{c[i][j]=c[i-1][j-1]+c[i-1][j];
	c[i][j]=(c[i][j]>=mod?c[i][j]-mod:c[i][j]);
	}
	}
	for (i=2;i<=n+1;i++)
	{for (j=0;j<=k;j++)
	{for (l=1;l<i;l++)
	{int wys=1ll*c[i-2][l-1]*dp[i-l][j]%mod;
	wys=1ll*wys*s[l][j+1]%mod;
	dp[i][j]=add(dp[i][j],wys);
	}
	}
	s[i][k]=dp[i][k];
	for (j=k-1;j>=0;j--) s[i][j]=add(s[i][j+1],dp[i][j]);
	}
	printf ("%d\n",dp[n+1][0]);
	return 0;
}
	
	