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;

LL n,m,k;

LL ncr[305][305];

LL dp[305][305],sum[305][305];  // size, root

int main()
{
    cin>>n>>k>>m;
    for(int i=0;i<=n+1;i++)
    {
        ncr[i][0]=ncr[i][i]=1;
        for(int j=1;j<i;j++)ncr[i][j]=(ncr[i-1][j-1]+ncr[i-1][j])%m;
    }

    for(int i=0;i<=k;i++)
    {
        dp[1][i]=1;
        sum[1][i]=(k-i+1)%m;
    }

    for(int sz=2;sz<=n+1;sz++)
    {
        for(int root=0;root<=k;root++)
        {
            for(int x=1;x<sz;x++)dp[sz][root]+=(((dp[sz-x][root]*sum[x][root+1])%m)*ncr[sz-2][x-1])%m;
            dp[sz][root]%=m;

        }
        for(int root=k;root>=0;root--) sum[sz][root]=(dp[sz][root]+sum[sz][root+1])%m;
    }
    cout<<dp[n+1][0]<<endl;
    return 0;

}
