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;

typedef long long ll;
typedef pair<int,int> pii;

const int maxn=307;

int n,k,m,f[maxn][maxn],g[maxn][maxn],C[maxn][maxn];

int main(){
	scanf("%d%d%d",&n,&k,&m);
	C[0][0]=1;
	for(int i=1;i<maxn;++i){
		for(int j=1;j<maxn;++j)
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%m;
		C[i][0]=1;
	}
	for(int i=0;i<=k;++i)f[1][i]=1,g[1][i]=k-i+1;
	for(int i=2;i<=n+1;++i){
		for(int j=0;j<=k;++j){
			for(int t=1;t<i;++t)
				f[i][j]=(f[i][j]+1ll*f[t][j]*g[i-t][j+1]%m*C[i-2][t-1])%m;
//			printf("f[%d][%d]=%d\n",i,j,f[i][j]);
		}
		for(int j=k;j>=0;--j)g[i][j]=(g[i][j+1]+f[i][j])%m; 
	}
	printf("%d\n",f[n+1][0]);
	return 0;
}
/*
4 3 999999999

150 150 998244353
*/
