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>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
const int N=310;
int C[N][N],f[N][N],s[N][N];
int main() {
    int n,k,Mo;
    cin>>n>>k>>Mo;
    for(int i=0;i<=n;i++)
	for(int j=C[i][0]=1;j<=i;j++)
	    C[i][j]=(C[i-1][j]+C[i-1][j-1])%Mo;
    for(int i=0;i<=k;i++) f[i][0]=1;
    for(int i=1;i<=n;i++) {
	for(int j=k;j;j--)
	    s[j][i-1]=(s[j+1][i-1]+f[j][i-1])%Mo;
	for(int j=0;j<=k;j++)
	    for(int p=0;p<i;p++)
		f[j][i]=(f[j][i]+1LL*s[j+1][p]*f[j][i-1-p]%Mo*C[i-1][p])%Mo;
    }
    cout<<f[0][n];
    return 0;
}