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=510;
int f[N][N],sum[N][N];
int n,mod,k;
int C[N][N];
void init()
{
	for(int i=0;i<N;i++)
		C[i][0]=C[i][i]=1;
	for(int i=1;i<N;i++)
		for(int j=1;j<i;j++)
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;
}
int main()
{
	scanf("%d%d%d",&n,&k,&mod);
	init();
	for(int i=0;i<=k;i++)
		f[1][i]=1;
	for(int j=k;j>=0;j--)
		sum[1][j]=(sum[1][j+1]+f[1][j])%mod;
	for(int i=2;i<=n+1;i++)
		for(int j=k;j>=0;j--)
		{
			for(int sz=1;sz<i;sz++)
				f[i][j]=(f[i][j]+1ll*f[i-sz][j]*sum[sz][j+1]%mod*C[i-2][sz-1])%mod;
			sum[i][j]=(sum[i][j+1]+f[i][j])%mod;
		}
	printf("%d\n",f[n+1][0]);
	return 0;
}
