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>
using namespace std;
#define N 305
int n,m,p,dp[N][N],su[N][N],c[N][N];
int main()
{
	scanf("%d%d%d",&n,&m,&p);n++;m++;
	for(int i=1;i<=m;i++)dp[1][i]=1,su[1][i]=i;
	for(int i=0;i<=n;i++)c[i][i]=c[i][0]=1;
	for(int i=2;i<=n;i++)for(int j=1;j<i;j++)c[i][j]=(c[i-1][j-1]+c[i-1][j])%p;
	for(int i=2;i<=n;i++)
	{
		for(int k=1;k<=m;k++)
		for(int j=1;j<i;j++)
		dp[i][k]=(dp[i][k]+1ll*dp[i-j][k]*su[j][k-1]%p*c[i-2][j-1])%p;
		for(int k=1;k<=m;k++)su[i][k]=(su[i][k-1]+dp[i][k])%p;
	}
	printf("%d\n",dp[n][m]);
}//