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>
#define N 305 
using namespace std;
int n,k,mod;
int c[N][N],f[N][N],sum[N][N];

int main()
{
	cin>>n>>k>>mod;
	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] + c[i - 1][j - 1]) % mod;
	}
	for(int i=0;i<=k;++i) f[1][i] = 1,sum[1][i] = k - i + 1;
	for(int i=2;i<=n + 1;++i)
	{
		for(int j=k;j>=0;--j)
		{
			for(int t = i - 1;t;--t)
			{
				f[i][j] = (f[i][j] + 1ll * f[i - t][j] * c[i - 2][t - 1]  % mod * sum[t][j + 1] % mod) % mod;
			}
			sum[i][j] = (sum[i][j + 1] + f[i][j]) % mod;
		}
	}
	cout<<f[n + 1][0]<<endl;
	return 0;
}