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;

typedef long long ll;

int MOD;

ll C[305][305];
int f[305][305],sum[305][305];

void pre(int n) {
  for(int i=0;i<=n;i++) C[i][0]=1;
  for(int i=1;i<=n;i++)
    for(int j=1;j<=i;j++) C[i][j]=(C[i-1][j-1]+C[i-1][j])%MOD;
}

int main() {
  int n,k;
  scanf("%d%d%d",&n,&k,&MOD);
  pre(n);
  for(int i=1;i<=k+1;i++) {
  	f[0][i]=1;
  	sum[0][i]=i;
  }
  for(int i=1;i<=n;i++) {
  	for(int j=1;j<=k+1;j++)
  	  for(int l=1;l<=i;l++) 
		f[i][j]=(f[i][j]+(ll)sum[l-1][j-1]*f[i-l][j]%MOD*C[i-1][l-1])%MOD;
  	for(int j=1;j<=k+1;j++) sum[i][j]=(sum[i][j-1]+f[i][j])%MOD;
  }
  printf("%d\n",f[n][k+1]);
  return 0;
}