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;
typedef long long LL;
typedef pair<int, int> P;
template<typename T> inline void chkmin(T &a, const T &b) { a = a < b ? a : b; }
template<typename T> inline void chkmax(T &a, const T &b) { a = a > b ? a : b; }

const int MAXN = 305;
int C[MAXN][MAXN], f[MAXN][MAXN], n, m, MOD;

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