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>
#include<algorithm>
using namespace std;
const int N=305;
int n,m,mod,C[N][N],f[N][N],g[N][N];
int main(){
	scanf("%d%d%d",&n,&m,&mod);++n;++m;
	for(int i=C[0][0]=1;i<=n;++i)
		for(int j=C[i][0];j<=i;++j)
			C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
	for(int i=1;i<=m;++i)f[1][i]=1,g[1][i]=i;
	for(int i=2;i<=n;++i)
		for(int j=1;j<=m;++j){
			for(int k=1;k<i;++k)
				f[i][j]=(f[i][j]+1ll*g[k][j-1]*f[i-k][j]%mod*C[i-2][k-1])%mod;
			g[i][j]=(g[i][j-1]+f[i][j])%mod;
		}
	printf("%d\n",f[n][m]);
	return 0;
}
