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>

typedef long long int int64;
int n,k;
int64 m;
int64 coe[303][303];
int64 dp[303][303];

int main()
{
	scanf("%d%d%lld",&n,&k,&m);
	coe[0][0] = 1;
	for(int i = 1;i <= n;++i) {
		coe[i][0] = 1;
		for(int j = 1;j <= i;++j) {
			coe[i][j] = (coe[i-1][j-1]*(i-j+1)+coe[i-1][j])%m;
		}
	}
	for(int j = 0;j <= k;++j) {
		dp[0][j] = 1;
	}
	for(int i = 1;i <= n;++i) {
		for(int j = 1;j <= k;++j) {
			int64 val = 0;
			for(int c = 0;c <= i;++c) {
				val += dp[i-c][j-1] * coe[i][c] % m;
			}
			dp[i][j] = val % m;
		}
	}
	printf("%lld\n", dp[n][k]);
}
