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;

ll n, k, p, dp[505][505], comb[505][505];

int main() {
	cin >> n >> k >> p;
	for (int i = 0; i < 505; ++i)
		for (int j = 0; j <= i; ++j) {
			if (j == 0)
				comb[i][j] = 1;
			else
				comb[i][j] = (comb[i-1][j] + comb[i-1][j-1])%p;
		}

	for (int i = 1; i <= n+1; ++i)
		for (int j = k; j >= 0; --j) {
			if (i == 1) {
				dp[i][j] = 1 + dp[i][j+1];
				continue;
			}
			dp[i][j] = dp[i][j+1];
			for (int l = 0; l < i-1; ++l) {
				dp[i][j] = (dp[i][j] + comb[i-2][l]*dp[l+1][j+1]%p*(dp[i-l-1][j] + p - dp[i-l-1][j+1]))%p;
			}
		}

	cout << (p + dp[n+1][0] - dp[n+1][1])%p << endl;
}