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;
using Int = long long;

//INSERT ABOVE HERE
Int co[303][303];
Int dp[303][303];

signed main(){
  Int n,k,mod;
  cin>>n>>k>>mod;
  memset(co,0,sizeof(co));
  co[0][0]=1;
  for(Int i=0;i<=n;i++){
    for(Int j=0;j<=n;j++){
      Int t=1;
      for(Int l=0;l<=j;l++){
	co[i+1][j]+=co[i][j-l]*t%mod;
	co[i+1][j]%=mod;
	t=t*(i+1)%mod;
      }
    }
  }
  
  memset(dp,0,sizeof(dp));
  dp[0][0]=1;
  for(Int i=0;i<k;i++){
    for(Int j=0;j<=n;j++){
      for(Int l=0;j+l<=n;l++){
	dp[i+1][j+l]+=dp[i][j]*co[j+1][l]%mod;
	dp[i+1][j+l]%=mod;
      }
    }
  }
  
  cout<<dp[k][n]<<endl;
  return 0;
}
