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;
#define ll long long
const int N=305;
int f[N][N],s[N][N],C[N][N],n,m,p;
int main()
{
    scanf("%d%d%d",&n,&m,&p);
    C[0][0]=1;
    for(int i=1;i<=n;i++)
    {
        C[i][0]=C[i][i]=1;
        for(int j=1;j<n;j++)C[i][j]=(C[i-1][j-1]+C[i-1][j])%p;
    }
    for(int i=0;i<=m;i++)f[1][i]=1,s[1][i]=m-i+1;
    for(int i=2;i<=n+1;i++)
    {
        for(int j=0;j<=m;j++)
            for(int l=1;l<i;l++)
                f[i][j]=(f[i][j]+1ll*C[i-2][l-1]*f[i-l][j]%p*s[l][j+1])%p;
        for(int j=m;j>=0;j--)s[i][j]=(s[i][j+1]+f[i][j])%p;
    }
    printf("%d\n",f[n+1][0]);
}
