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<cstdio>
int N,K,M,f[310][310][310];
int main(){
	scanf("%d%d%d",&N,&K,&M);
	f[0][1][0]=1;
	for(int i=0;i<=N;i++){
		for(int j=1;j<=K;j++){
			for(int k=i;k>=0;k--)if(f[i][j][k]){
				if(k)(f[i][j][k-1]+=f[i][j][k])%=M;
				else(f[i][j+1][i]+=f[i][j][k])%=M;
				f[i+1][j][k]=(f[i+1][j][k]+(k+1ll)*f[i][j][k])%M;
			}
		}
	}
	printf("%d\n",f[N][K+1][N]);
}