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;

#define X first
#define Y second

const int N=3e2+10;

int n,m,MOD;
ll f[N][N][N];


ll DP(int cur,int len,int pos){
        if (len>n) return 0;
        if (cur>m) return len==n;
        ll &ans=f[cur][len][pos];
        if (ans!=-1) return ans;
        ans=(pos+1)*DP(cur,len+1,pos)%MOD;
        if (pos==0) ans=(ans+DP(cur+1,len,len))%MOD;
        else ans=(ans+DP(cur,len,pos-1))%MOD;
        return ans;
}
int main(){
        cin>>n>>m>>MOD;
        memset(f,-1,sizeof(f));
        cout<<DP(1,0,0);
}
