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;

const int N=305;

typedef long long LL;

int n,m,mo,f[N][N],s[N][N],ss[N][N],C[N][N],ans;

int main()
{
	scanf("%d%d%d",&n,&m,&mo); n++;
	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-1]+C[i-1][j])%mo;
	}
	f[1][0]=1;
	for (int i=0;i<=m;i++) s[1][i]=1,ss[1][i]=(i+1)%mo;
	for (int i=2;i<=n;i++)
	{
		for (int j=1;j<=m;j++)
		{
			for (int x=1;x<i;x++) f[i][j]=(f[i][j]+(LL)s[x][j]*ss[i-x][j-1]%mo*C[i-2][x-1])%mo;
		}
		for (int j=m;j;j--) f[i][j]=((LL)f[i][j]-f[i][j-1])%mo;
		for (int j=1;j<=m;j++)
		{
			s[i][j]=(s[i][j-1]+f[i][j])%mo; ss[i][j]=(ss[i][j-1]+s[i][j])%mo;
		}
	}
	for (int i=1;i<=m;i++) ans=(ans+f[n][i])%mo;
	if (ans<0) ans+=mo;
	printf("%d\n",ans);
	return 0;
}