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,mo,k,c[N][N],f[N][N],w[N][N];
int main(){
    cin>>n>>k>>mo;
    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-1]+c[i-1][j])%mo;
    }
    for (int i=k; i>=0; --i){
	f[i][0]=1;
	for (int j=1; j<=n; ++j)
	    for (int t=0; t<j; ++t)
		(f[i][j]+=1ll*w[i+1][j-t-1]*f[i][t]%mo*c[j-1][t]%mo)%=mo;
	for (int j=0; j<=n; ++j)
	    w[i][j]=(w[i+1][j]+f[i][j])%mo;
    }
    cout<<f[0][n];
    return 0;
}
