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 n,K,md;
int dp[310][310];
int C[310][310];
void Add(int &x,int y){
	(x+=y)%=md;
}
int main(){
	scanf("%d%d%d",&n,&K,&md);
	C[0][0]=C[1][0]=C[1][1]=1;
	for(int i=2;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])%md;
	}
	for(int i=0;i<=K;i++)
		dp[1][i]=1;
	int sum;
	for(int i=2;i<=n+1;i++){
		for(int j=1;j<i;j++){
			sum=0;
			for(int k=K;k>=0;k--){
				Add(dp[i][k],sum*(long long)(i-j==1?1:C[i-2][j-1])%md*dp[i-j][k]%md);
				Add(sum,dp[j][k]);
			}
		}
	}
	printf("%d\n",dp[n+1][0]);
	return 0;
}
