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;
#define mod 998244353
#define MOD 1000000007
#define inf 0x3f3f3f3f
#define linf 0x3f3f3f3f3f3f3f3fll
typedef long long ll;
typedef pair<int,int> pii;
typedef unsigned long long ull;
int dp[330][330];
int C[330][330];
int main()
{
	int n,k,m;
	cin>>n>>k>>m;
	C[0][0]=1;
	for(int i=1;i<330;i++)
	{
		C[i][0]=C[i][i]=1;
		for(int j=1;j<i;j++)
			C[i][j]=(C[i-1][j]+C[i-1][j-1])%m;
	}
	for(int i=0;i<=k;i++)
		dp[0][i]=1;
	for(int i=1;i<=n;i++)
	{
		dp[i][1]=1;
		for(int j=2;j<=k;j++)
		{
			dp[i][j]=dp[i][j-1];
			for(int lsz=1;lsz<=i;lsz++)
			{
				dp[i][j]=(dp[i][j]+dp[lsz-1][j-1]*1ll*dp[i-lsz][j]%m*1ll*C[i][lsz-1]%m)%m;
			}
		}
	}
	cout<<dp[n][k]<<endl;
	return 0;
}