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;

ll D[333][333], K[333][333][333];
ll dp[333][333];
ll n, t, m;

int main()
{
	ll i, j, k;
	
	scanf("%lld%lld%lld", &n, &t, &m);
	
	D[0][0] = K[0][0][0] = 1;
	for(i=1;i<=n;i++){
		for(j=0;j<=i;j++){
			for(k=0;k<=j;k++){
				if(j < i){
					K[i][j][k] = (K[i][j][k] + K[i-1][j][k]) % m;
				}
				if(j){
					K[i][j][k] = (K[i][j][k] + K[i-1][j-1][k] * k) % m;
					if(i-j >= k-1) K[i][j][k] = (K[i][j][k] + K[i-1][j-1][k-1] * (i-j-k+2)) % m;
				}
				D[i][j] = (D[i][j] + K[i][j][k]) % m;
			}
		}
	}
	
	for(i=0;i<=n;i++) dp[1][i] = 1;
	
	for(i=2;i<=t;i++){
		for(j=0;j<=n;j++){
			for(k=0;k<=j;k++){
				dp[i][j] = (dp[i][j] + dp[i-1][j-k] * D[j][k]) % m;
			}
		}
	}
	
	printf("%lld\n", dp[t][n]);
	
	return 0;
}