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<iostream>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<cstdio>
using namespace std;

const int N=305;

int n,m,mod;
int dp[N][N],c[N][N],s[N][N];

void init(int n){
	int i,j;
	c[0][0]=1;
	for (i=1;i<=n;i++){
		c[i][0]=1;
		for (j=1;j<=i;j++) c[i][j]=(c[i-1][j]+c[i-1][j-1])%mod;
	}
}

int main(){
	int i,j,k;
	scanf("%d%d%d",&n,&m,&mod);
	init(300);
	for (i=0;i<=m;i++) dp[1][i]=1;
	for (i=m;i>=0;i--) s[1][i]=(s[1][i+1]+dp[1][i])%mod;
	for (i=2;i<=n+1;i++){
		for (j=0;j<=m;j++)
			for (k=1;k<i;k++){
				(dp[i][j]+=1ll*dp[i-k][j]*s[k][j+1]%mod*c[i-2][k-1]%mod)%=mod;
			}
		for (j=m;j>=0;j--) s[i][j]=(s[i][j+1]+dp[i][j])%mod;
	}
	printf("%d\n",dp[n+1][0]);
	return 0;
}