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>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
using namespace std;

typedef long long LL;

const int maxn=305;

int n,k;
LL mo;

LL C[maxn][maxn];
void Pre(int n)
{
	fo(i,0,n)
	{
		C[i][0]=1;
		fo(j,1,i) C[i][j]=(C[i-1][j-1]+C[i-1][j])%mo;
	}
}

LL f[maxn][maxn],sf[maxn][maxn];
int main()
{
	scanf("%d %d %lld",&n,&k,&mo);
	
	Pre(n);
	
	fo(j,0,k) f[1][j]=1, sf[1][j]=k-j+1;
	fo(i,2,n+1)
	{
		fo(j,0,k)
		{
			fo(sz,1,i-1) (f[i][j]+=f[i-sz][j]*sf[sz][j+1]%mo*C[i-2][sz-1])%=mo;
		}
		sf[i][k]=f[i][k];
		fd(j,k-1,1) sf[i][j]=(sf[i][j+1]+f[i][j])%mo;
	}
	
	printf("%lld\n",f[n+1][0]);
}