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 <iostream>
#include <cstdio>
#define int long long
#define N 3002
using namespace std;
int n,mod,k,i,j,size,C[N][N],f[N][N],sum[N][N];
int read()
{
	char c=getchar();
	int w=0;
	while(c<'0'||c>'9') c=getchar();
	while(c<='9'&&c>='0'){
		w=w*10+c-'0';
		c=getchar();
	}
	return w;
}
signed main()
{
	n=read();k=read();mod=read();
	C[0][0]=1;
	for(i=1;i<=n+2;i++){
		C[i][0]=1;
		for(j=1;j<=n+2;j++) C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;
	}
	for(i=k;i>=0;i--) f[1][i]=1,sum[1][i]=(sum[1][i+1]+1)%mod;
	for(i=2;i<=n+1;i++){
		for(j=0;j<=k;j++){
			for(size=1;size<i;size++){
				f[i][j]=(f[i][j]+f[i-size][j]*C[i-2][size-1]%mod*sum[size][j+1]%mod)%mod;
			}
		}
		for(j=k;j>=0;j--) sum[i][j]=(sum[i][j+1]+f[i][j])%mod;
	}
	printf("%lld\n",f[n+1][0]);
	return 0;
}
