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>
#define ll long long
using namespace std;
ll n,m,p,k,i,j,mx,f[302][302],c[302][302],g[302][302];
int main(){
	scanf("%lld%lld%lld",&n,&mx,&p);
	for(i=0;i<=n;i++)c[i][0]=1;
	for(i=1;i<=n;i++)
	 for(j=1;j<=i;j++)c[i][j]=(c[i-1][j]+c[i-1][j-1])%p;
	f[0][0]=g[0][0]=1;
	for(j=1;j<=mx;j++)f[0][j]=1,g[0][j]=j+1;
	for(i=1;i<=n;i++){
		for(j=1;j<=mx;j++){
			for(k=1;k<=i;k++){
				f[i][j]=(f[i][j]+g[k-1][j-1]*f[i-k][j]%p*c[i-1][k-1])%p;
			}
			g[i][j]=(g[i][j-1]+f[i][j])%p;
			//printf("%lld %lld %lld\n",i,j,f[i][j]);
		}
	}
	printf("%lld",f[n][mx]);
}