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;
int f[309][309],C[309][309],S[309][309];
int main(){
  int n,m,mod;
  scanf("%d%d%d",&n,&m,&mod);
  for(int i=0;i<=n;i++)
    for(int j=0;j<=i;j++)
      C[i][j]=(j==0||j==i)?1:(C[i-1][j-1]+C[i-1][j])%mod;
  for(int i=0;i<=m;i++) f[1][i]=1;
  for(int i=2;i<=n+1;i++){
    for(int j=m;j>=0;j--) S[i-1][j]=(S[i-1][j+1]+f[i-1][j])%mod;
    for(int j=0;j<=m;j++)
      for(int k=1;k<i;k++)
	f[i][j]=(1ll*f[i-k][j]*C[i-2][k-1]%mod*S[k][j+1]+f[i][j])%mod;
  }
  printf("%d",f[n+1][0]);
  return 0;
}
