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, m, mod, dp[307][307][307];
int main()
{
	cin >> n >> m >> mod;
	dp[0][1][0] = 1;
	for (int i = 0; i <= n; i++)
		for (int j = 1; j <= m; j++)
			for (int k = i; k >= 0; k--)
			{
				if (k)dp[i][j][k - 1] = (dp[i][j][k - 1] + dp[i][j][k]) % mod;
				else dp[i][j + 1][i] = (dp[i][j + 1][i] + dp[i][j][k]) % mod;
				dp[i + 1][j][k] = (dp[i + 1][j][k] + 1LL * (k + 1) * dp[i][j][k] % mod) % mod;
			}
	cout << dp[n][m][0] << endl;
	return 0;
}