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;
const int N=305;
int n,m,mod,f[N][N],sum[N][N],C[N][N];
int main(){
	scanf("%d%d%d",&n,&m,&mod);
	C[0][0]=1;
	for(int i=1;i<=300;C[i++][0]=1)
		for(int j=1;j<=i;j++)
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;
	for(int i=0;i<=m;i++)f[1][i]=1;
	sum[1][0]=f[1][0];
	for(int i=1;i<=m;i++)sum[1][i]=(sum[1][i-1]+f[1][i])%mod;
	for(int i=2;i<=n+1;i++){
		for(int j=0;j<=m;j++){
			for(int k=1;k<i;k++){
				f[i][j]=(f[i][j]+1ll*C[i-2][k-1]*(sum[k][m]-sum[k][j])%mod*f[i-k][j])%mod;
			}
		}
		sum[i][0]=f[i][0];
		for(int j=1;j<=m;j++)sum[i][j]=(sum[i][j-1]+f[i][j])%mod;
	}
	cout<<(f[n+1][0]+mod)%mod<<"\n";
}