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 N = 305;

int n, m, mod;
int c[N][N];
int f[N][N];
int g[N][N];
int h[N][N];

void add(int &x, int y) { x += x + y >= mod ? y - mod : y; }

int main() {
	cin >> n >> m >> mod;
	for (int i = 0; i < N; ++i) c[i][0] = 1;
	for (int i = 1; i < N; ++i) {
		for (int j = 1; j <= i; ++j) {
			c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
		}
	}
	for (int i = 1; i <= m + 1; ++i) h[0][i] = 1;
	for (int i = 1; i <= n; ++i) {
		for (int j = m; j >= 1; --j) {
			f[i][j] = h[i - 1][j + 1];
			g[i][j] = (g[i][j + 1] + f[i][j]) % mod;
		}
		for (int j = 1; j <= m; ++j) {
			for (int k = 1; k <= i; ++k) {
				add(h[i][j], 1LL * h[i - k][j] * g[k][j] % mod * c[i - 1][k - 1] % mod);
			}
		}
	}
	cout << h[n][1];
}