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<cstdlib>
#include<cstring>
#include<algorithm>

typedef long long LL;

const int N=305;

int n,k,MOD,f[N][N],s[N][N],c[N][N];

int main()
{
    scanf("%d%d%d",&n,&k,&MOD);
    c[0][0]=1;
    for (int i=1;i<=n;i++)
    {
        c[i][0]=1;
        for (int j=1;j<=i;j++)
            c[i][j]=(c[i-1][j]+c[i-1][j-1])%MOD;
    }
    for (int i=0;i<=k;i++) f[1][i]=1,s[1][i]=k-i+1;
    for (int i=2;i<=n+1;i++)
    {
        for (int j=0;j<=k;j++)
            for (int l=1;l<i;l++)
                (f[i][j]+=(LL)f[i-l][j]*s[l][j+1]%MOD*c[i-2][l-1]%MOD)%=MOD;
        for (int j=k;j>=0;j--) s[i][j]=(s[i][j+1]+f[i][j])%MOD;
    }
    printf("%d",f[n+1][0]);
    return 0;
}