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 maxn = 305;

int n, m, mod;
ll ans, c[maxn][maxn], dp[maxn][maxn], f[maxn][maxn];

void init()
{
	c[0][0] = 1;
	for(int i = 1; i <= n; ++i)
	{
		c[i][0] = 1;
		for(int j = 1; j <= i; ++j)
			c[i][j] = (c[i-1][j] + c[i-1][j-1]) % mod;
	}
}

int main()
{
	scanf("%d%d%d", &n, &m, &mod);
	init();
	for(int i = 0; i <= m; ++i)
		dp[1][i] = 1;
	for(int i = 1; i <= n + 1; ++i)
	{
		for(int j = 0; j <= m; ++j)
		{
			for(int k = 1; k < i; ++k)
				dp[i][j] = (dp[i][j] + ((dp[i-k][j] * f[k][j+1] % mod) * c[i-2][k-1] % mod)) % mod;
		}
		for(int j = m; j >= 0; --j)
			f[i][j] = (f[i][j+1] + dp[i][j]) % mod;
	}
	printf("%lld", dp[n+1][0]);
	return 0;
}
