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,_e=b;i<=_e;++i)
#define ll long long
using namespace std;
const int N=305;
int n,k,mo,v,f[N][N],f2[N][N];
int main(){
	cin>>n>>k>>mo;
	f2[0][0]=1;
	fo(i,1,n+1){
		f2[i][0]=1;
		fo(j,1,n)
			f2[i][j]=((ll)f2[i][j-1]*i+f2[i-1][j])%mo;
	}
	f[0][1]=1;
	fo(i,1,k){
		fo(j,1,n+1)if(v=f[i-1][j]){
			fo(l,0,n+1-j)
				f[i][j+l]=((ll)v*f2[j][l]+f[i][j+l])%mo;
		}
	}
	cout<<f[k][n+1];
}