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 ri register int
const int N=305;
int dp[N][N],sdp[N],c[N][N];
int main(){
	ri n,k,mod,s,t,i,j;
	scanf("%d%d%d",&n,&k,&mod);
	for(i=0;i<=n+1;++i){
		c[i][0]=1;
		for(j=1;j<=i;++j)
			c[i][j]=(c[i-1][j-1]+c[i-1][j])%mod;
	}
	for(i=k;i>=0;--i){
		dp[i][1]=1;
		for(s=1;s<=n+1;++s){
			for(t=1;t<s;++t)
				dp[i][s]=(dp[i][s]+(long long)dp[i][s-t]*sdp[t]%mod*c[s-2][t-1])%mod;
		//	printf("dp %d %d %d\n",i,s,dp[i][s]);
		}
		for(s=1;s<=n+1;++s)
			sdp[s]=(sdp[s]+dp[i][s])%mod;
	}
	printf("%d\n",dp[0][n+1]);
	return 0;
}