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;
typedef long long ll;
typedef pair<int,int> P;

int n,k;
ll m;
ll dp[305][305];
ll dp2[305][305];

int main(void){
	scanf("%d%d%lld",&n,&k,&m);
	dp2[0][0]=1;
	for(int i=0;i<=n;i++){
		for(int j=0;j<=n;j++){
			dp2[i+1][j]+=dp2[i][j];
			dp2[i+1][j]%=m;
			dp2[i+1][j+1]+=(ll)dp2[i][j]*(i+1-j)%m;
			dp2[i+1][j+1]%=m;
		}
	}
	dp[0][0]=1;
	for(int i=0;i<=n;i++){
		dp[1][i]=1;
	}
	for(int i=1;i<=k;i++){
		for(int j=0;j<=n;j++){
			for(int k=0;k<=n-j;k++){
				dp[i+1][j+k]+=dp[i][j]*dp2[j+k][k]%m;
				dp[i+1][j+k]%=m;
			}
		}
	}
	printf("%lld\n",dp[k][n]);
	return 0;
}