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>
const int N=305;
int n,k,mo,i,j,l,C[N][N],f[N][N],g[N][N],ans;
int main(){
	scanf("%d%d%d",&n,&k,&mo);
	for(i=**C=1;i<N;++i)for(j=*C[i]=1;j<=i;++j)C[i][j]=(C[i-1][j-1]+C[i-1][j])%mo;
	f[k+1][0]=1;
	for(i=k;i;--i){
		for(j=1;j<=n;++j)g[i][j]=(g[i+1][j]+f[i+1][j-1])%mo;
		f[i][0]=1;
		for(j=1;j<=n;++j)for(l=1;l<=j;++l)f[i][j]=(f[i][j]+1ll*f[i][j-l]*g[i][l]%mo*C[j-1][l-1])%mo;
	}
	printf("%d\n",f[1][n]);
	return 0;
}