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;

const int N = 305;

int n, K, mod, C[N][N], S[N][N], F[N][N];

int main()
{
	scanf("%d%d%d", &n, &K, &mod);
	for (int i = 0; i <= max(n, K); i++)
	{
		C[i][0] = 1;
		for (int j = 1; j <= i; j++)
			C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
	}
	F[0][0] = 1;
	for (int i = K; i >= 0; i--)
	{
		F[1][i] = 1;
		S[1][i] = (S[1][i + 1] + 1) % mod;
	}
	for (int i = 2; i <= n + 1; i++)
	{
		for (int j = 0; j <= K; j++)
			for (int a = 1; a < i; a++)
				F[i][j] = (F[i][j] + (ll)F[i - a][j] * S[a][j + 1] % mod * C[i - 2][a - 1] % mod) % mod;
		for (int j = K; j >= 0; j--)
			S[i][j] = (S[i][j + 1] + F[i][j]) % mod;
	}
	printf("%d\n", F[n + 1][0]);
	return 0;
}