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<cstdio>
int P,f[307][307][307];
void inc(int&a,int b){a+=b-P,a+=a>>31&P;}
int main()
{
    int n,m;scanf("%d%d%d",&n,&m,&P),f[0][1][0]=1;
    for(int i=0;i<=n;++i) for(int j=1;j<=m;++j) for(int k=i;~k;--k) k? inc(f[i][j][k-1],f[i][j][k]):inc(f[i][j+1][i],f[i][j][k]),inc(f[i+1][j][k],(k+1ll)*f[i][j][k]%P);
    printf("%d",f[n][m][0]);
}
