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;
int n, l, p, f[320][320];
int main() {
	scanf("%d%d%d", &n, &l, &p);
	f[0][0] = 1;
	for (int i = 0; i <= n; i++) {
		for (int j = 0; j < l; j++) {
			for (int k = i; k >= 0; k--) {
				if (k) {
					f[j][k - 1] = (f[j][k - 1] + f[j][k]) % p;
				} else {
					f[j + 1][i] = (f[j + 1][i] + f[j][k]) % p;
				}
				f[j][k] = f[j][k] * (k + 1LL) % p;
			}
		}
	}
	printf("%d\n", f[l][n]);
	return 0;
}