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
#pragma GCC optimize(2)
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define R register int
const ll N=333;
int n,k;
ll c[N][N],m,f[N][N],g[N][N];
#define add(a,b) (((a)+(b))%m)
#define mul(a,b) ((a)*(b)%m)
int main(){
    scanf("%d%d%lld",&n,&k,&m);++n;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]=add(c[i-1][j-1],c[i-1][j]);
    }
    for(int i=k;~i;i--)f[1][i]=1,g[1][i]=g[1][i+1]+1;
    for(int i=2;i<=n;i++)for(int x=k;~x;x--){
        for(int j=1;j<i;j++)f[i][x]=add(f[i][x],mul(mul(g[j][x+1],f[i-j][x]),c[i-2][j-1]));
        g[i][x]=add(f[i][x],g[i][x+1]);
    }
    //for(int i=1;i<=n;i++)for(int j=1;j<=i&&j<=k;j++)f[i]=add(f[i],mul(mul(c[k][j],c[i-1][j-1]),f[i-j]));
    printf("%lld",f[n][0]);
    return 0;
}