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;
int n,k,mo;
int f[N][N];
int c[N][N];
int g[N];
int main(){
	scanf("%d%d%d",&n,&k,&mo);
	for (int i=0;i<=k+1;i++) f[0][i]=1;
	for (int i=0;i<=n;i++){
		c[i][0]=1;
		for (int j=1;j<=i;j++)
			c[i][j]=(c[i-1][j]+c[i-1][j-1])%mo; 
	}
	for (int j=k;j>=0;j--){
		memset(g,0,sizeof(g));
		g[0]=1;
		for (int p=1;p<=n;p++)
			for (int q=1;q<=p;q++)
				g[p]=(g[p]+1ll*g[p-q]*c[p-1][q-1]%mo*f[q][j+1]%mo)%mo;
		for (int i=1;i<=n+1;i++)
			f[i][j]=(f[i][j+1]+g[i-1])%mo;
	}
	printf("%d\n",(f[n+1][0]-f[n+1][1]+mo)%mo);
}