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<cstdio>
#define ll long long
using namespace std;
int n,m,mod;
ll c[1010][1010],f[1010][1010],s[1010][1010];
int main(){
	scanf("%d%d%d",&n,&m,&mod);
	c[0][0]=1;
	for(register int i=1;i<=n;i++)for(register int j=0;j<=i;j++)c[i][j]=(c[i-1][j-1]+c[i-1][j])%mod;
	for(register int i=0;i<=m;i++)f[1][i]=1;
	for(register int i=m;~i;i--)s[1][i]=(s[1][i+1]+f[1][i])%mod;
	for(register int i=2;i<=n+1;i++){
		for(register int j=m;~j;j--){
			for(register int k=1;k<i;k++){
				f[i][j]=(f[i][j]+c[i-2][k-1]*f[i-k][j]%mod*s[k][j+1]%mod)%mod;
			}
			//cout<<"f["<<i<<"]["<<j<<"]="<<f[i][j]<<endl;
			s[i][j]=(s[i][j+1]+f[i][j])%mod;
		}
	}
	printf("%lld",f[n+1][0]);
	return 0;
}