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;
long long f[333][333][333];

long long solution(int n,int x,int y){
  f[0][1][0]=1;
  for(int i=0;i<=n;i++)
    for(int j=1;j<=x;j++)
      for(int p=i;p>=0;p--){
          if(p) (f[i][j][p-1]+=f[i][j][p]) %= y;
          else (f[i][j+1][i]+=f[i][j][p]) %= y;
          (f[i+1][j][p]+=f[i][j][p]*(p+1)) %= y;
      }
  return f[n][x + 1][n];
}

int main()
{
  int n, x ,y;
  n = 197;
  x = 73;
  y = 82195333;
  cin>>n>>x>>y;
  long long res = solution(n, x, y);
  cout<<res<<endl;
  return 0;
}
