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;
const int maxn = 300;
int n, K, mod;
int f[maxn + 10][maxn + 10], s[maxn + 10][maxn + 10], c[maxn + 10][maxn + 10];
int main() {
	scanf("%d%d%d", &n, &K, &mod);
	c[0][0] = 1;
	for (int i = 0; i <= maxn; ++i) {
		c[i][0] = 1;
		for (int j = 1; j <= i; ++j)
			c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
	}
	for (int i = 0; i <= K; ++i) f[1][i] = 1;
	for (int i = K; i >= 0; --i) s[1][i] = (s[1][i + 1] + f[1][i]) % mod;
	for (int i = 2; i <= n + 1; ++i) {
		for (int j = 0; j <= K; ++j)
			for (int k = 1; k < i; ++k) {
				(f[i][j] += 1ll * f[i - k][j] * s[k][j + 1] % mod * c[i - 2][k - 1] % mod) %= mod;
			}
		for (int j = K; j >= 0; --j)
			s[i][j] = (s[i][j + 1] + f[i][j]) % mod;
	}
	printf("%d", f[n + 1][0]);
}
