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;
typedef long long ll;
typedef pair<ll,ll> pll;
const ll MAX=303;
ll c[MAX][MAX],N,K,M,dp[MAX][MAX],dps[MAX][MAX];
ll comb(ll x,ll y){
    if(y==x||y==0) return 1;
    if(c[x][y]==-1){
        c[x][y]=(comb(x-1,y-1)+comb(x-1,y))%M;
    }
    return c[x][y];
}
int main(){
    scanf("%lld%lld%lld",&N,&K,&M);
    for(int i=0;i<=N;i++) for(int j=0;j<=N;j++) c[i][j]=-1;
    for(int i=0;i<=K;i++) dp[1][i]=1,dps[1][i]=K-i  ;
    for(int i=2;i<=N+1;i++){
        for(int j=K;j>=0;j--){
            // dp[i][j]
            for(int l=1;l<=i-1;l++){
                ll t=dp[l][j]*comb(i-2,l-1)%M;
                dp[i][j]+=t*dps[i-l][j];
                dp[i][j]%=M;
            }
            dps[i][j-1]=(dps[i][j]+dp[i][j])%M;
        }
    }
    printf("%lld\n",dp[N+1][0]);
}
