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, k, M, binom[305][305], f[305][305], sum[305][305];

int main() {
	scanf("%d%d%d", &n, &k, &M), ++n, ++k;
	for (int i = 0; i <= n; ++i)
		for (int j = binom[i][0] = 1; j <= i; ++j)
			binom[i][j] = (binom[i - 1][j] + binom[i - 1][j - 1]) % M;
	fill(f[1] + 1, f[1] + 1 + k, 1);
	for (int i = k - 1; i; --i)
		sum[1][i] = k - i;
	for (int i = 2; i <= n; ++i) {
		for (int x = 1; x <= k; ++x)
			for (int j = 1; j <= i - 1; ++j)
				f[i][x] = (f[i][x] + 1ll * f[i - j][x] * sum[j][x] % M * binom[i - 2][j - 1]) % M;
		for (int x = k - 1; x; --x)
			sum[i][x] = (sum[i][x + 1] + f[i][x + 1]) % M;
	}
	printf("%d\n", f[n][1]);
	return 0;
}
