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
#define N 320

int n,m,mod,c[N][N],f[N][N],g[N][N];

int main(){
	scanf("%d%d%d",&n,&m,&mod);
	c[0][0]=1;
	for (int i=1;i<=n+1;++i){
		c[i][0]=1;
		for (int j=1;j<=i;++j) c[i][j]=(c[i-1][j]+c[i-1][j-1])%mod;
	}
	for (int i=m;i>=0;--i){f[1][i]=1; g[1][i]=(g[1][i+1]+f[1][i])%mod;}
	for (int i=2;i<=n+1;++i){
		for (int j=0;j<=m;++j)
			for (int k=1;k<i;++k)
				f[i][j]=(f[i][j]+(LL)f[i-k][j]*g[k][j+1]%mod*c[i-2][k-1])%mod;
		for (int j=m;j>=0;--j) g[i][j]=(g[i][j+1]+f[i][j])%mod;
	}
	printf("%d\n",f[n+1][0]);
	
	return 0;
}
			