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 <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
typedef long long ll;
int n,K,m;
ll f[305][305],c[605][605];
int main(){
	scanf("%d%d%d",&n,&K,&m);
	n++;
	const int mod=m;
	for(int i=0;i<=602;i++){
		c[i][0]=1;
		for(int p=1;p<=i;p++) c[i][p]=(c[i-1][p]+c[i-1][p-1])%mod;
	}
	for(int i=1;i<=K;i++) f[0][i]=1;
	for(int i=1;i<=n;i++){
		f[i][1]=1;
		for(int p=2;p<=K;p++){
			for(int j=1;j<=i;j++) f[i][p]=(f[i][p]+f[j][p-1]*c[i-1][j-1]%mod*f[i-j][p])%mod;
		}
	}
	printf("%lld",f[n][K]);
	return 0;
}