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<cstdio>
#include<cstring>
#define inlien inline
#define retrun return
#define cpnst const
int F[333][333][333],n,m,mod;
inline void pre()
{
	register int i,ii,iii;
	for(i=0;i<=n;i++)
		for(ii=1;ii<=m;ii++)
			for(iii=i;~iii;iii--)
			{
				if(iii)(F[i][ii][iii-1]+=F[i][ii][iii])%=mod;
				else(F[i][ii+1][i]+=F[i][ii][iii])%=mod;
				int t=F[i][ii][iii]*1ll*(iii+1)%mod;
				(F[i+1][ii][iii]+=t)%=mod;
			}
}
int main()
{
	scanf("%d%d%d",&n,&m,&mod),F[0][1][0]=1;
	pre(),printf("%d\n",F[n][m][0]);
}
/*
Giving the world a better yourself is giving yourself a better world. 
*/