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 dp[303][303];
Int nx[303][303];

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