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<cstdio>
#define int long long
int n,m,mod,C[310][310],pre[310][310],f[310][310];
using namespace std;
signed main(){
	scanf("%lld%lld%lld",&n,&m,&mod);
	C[0][0]=1;
	for(int i=1;i<=n;i++){
		C[i][0]=C[i][i]=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,pre[1][i]=m-i+1;
    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-k][j]*pre[k][j+1]%mod*C[i-2][k-1])%=mod;
    	for(int j=m;j>=0;j--)
    		pre[i][j]=(pre[i][j+1]+f[i][j])%mod;
    }
    printf("%lld\n",f[n+1][0]);
} 