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;

int main(){
	LL n, k, MOD;
	cin >> n >> k >> MOD;
	LL numways[n+1][n+1];
	for(int i = 0; i <= n; i++){
		LL ways[i+1];
		for(int j = 0; j <= i; j++){
			ways[j] = 0;
		}
		ways[0] = 1;
		LL maxa = n-i;
		for(int a = 0; a <= maxa; a++){
			for(int j = 1; j <= i; j++){
				ways[j] += ways[j-1];
				ways[j] %= MOD;
			}
			numways[i][i+a] = ways[i];
			for(int j = 0; j <= i; j++){
				ways[j] *= (j + 1);
				ways[j] %= MOD;
			}
		}
		for(int j = 0; j < i; j++){
			numways[i][j] = 0;
		}
	}
	vector<LL> dp(n+1, 0);
	dp[0] = 1;
	for(int i = 1; i <= k; i++){
		vector<LL> newdp(n+1, 0);
		for(int j = 0; j <= n; j++){
			for(int r = 0; r <= n; r++){
				newdp[r] += dp[j] * numways[j][r];
				newdp[r] %= MOD;
			}
		}
		dp = newdp;
	}
	cout << dp[n] << endl;
}
