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 = 310;
ll f[maxn][maxn], c[maxn][maxn], sum[maxn][maxn];
ll mod;

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

int main()
{
	//freopen("E.in","r",stdin);
	int n,k;
	cin >> n >> k >> mod;

	init(n);

	for (int i=0;i<=k;i++) f[1][i] = 1, sum[1][i] = i+1;
	for (int i=2;i<=n+1;i++)
	{
		for (int j=0;j<=k;j++)
		{
			for (int t=1;t<=i-1;t++)
			{
				f[i][j] += c[i-2][t-1] * f[i-t][j] % mod * (sum[t][k] - sum[t][j] + mod) % mod;
				f[i][j] %= mod;
			}
			if (j >= 1) sum[i][j] = (sum[i][j-1] + f[i][j]) % mod;
			else sum[i][j] = f[i][j];
		}
	}

	cout << f[n+1][0] << endl;
	return 0;
}
