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 <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <string.h>
#include <stdlib.h>
#include <time.h>
#include <climits>

using namespace std;

const int maxN=307;

long long dp[maxN][maxN],s[maxN][maxN],c[maxN][maxN];

int main(){
	int n,m,k;
	scanf("%d%d%d",&n,&k,&m);

	for (int i=0;i<=n;i++) {
		c[i][0]=c[i][i]=1;
		for (int j=1;j<i;j++) c[i][j]=(c[i-1][j]+c[i-1][j-1])%m;
	}

	for (int i=0;i<=k;i++) dp[1][i]=1,s[1][i]=(k-i+1)%m;
	for (int i=2;i<=n+1;i++) 
		for (int j=k;j>=0;j--){
			for (int t=1;t<i;t++) dp[i][j]=(dp[i][j]+dp[i-t][j]*c[i-2][t-1]%m*s[t][j+1]%m)%m;
			s[i][j]=(s[i][j+1]+dp[i][j])%m;
		}

	printf("%lld\n",dp[n+1][0]);
	return 0;
}
