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 <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;
int n,k,mo;
int g[1001][1001],f[1001][1001];
int Sum(int x,int y) {
    x+=y;
    return (x>=mo)?x-mo:x;
}
int Mul(int x,int y) {
    return (long long)x*y%mo;
}
int main() {
    scanf("%d%d%d",&n,&k,&mo);
    g[0][0]=1;
    for (int i=1;i<=n;i++)
        for (int j=0;j<=i;j++) {
            g[i][j]=g[i-1][j];
            if (j) g[i][j]=Sum(g[i][j],Mul(g[i-1][j-1],i-j+1));
        }
    f[0][0]=1;
    for (int i=1;i<=k;i++)
        for (int j=0;j<=n;j++) {
            f[j][i]=0;
            for (int kx=0;kx<=j;kx++)
                f[j][i]=Sum(f[j][i],Mul(f[kx][i-1],g[j][j-kx]));
        }
    printf("%d\n",f[n][k]);
    return 0;
}
