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
#define N 666
ll M,f[N][N],s[N][N],ans,C[N][N];
ll n,K;
int main(){
    scanf("%lld%lld%lld",&n,&K,&M);
    C[0][0]=1;
    for (ll i=1;i<=n;i++){
        C[i][0]=1;
        for (ll j=1;j<=i;j++) 
            (C[i][j]=C[i-1][j-1]+C[i-1][j])%=M;
    }
    for (ll i=0;i<=K;i++) f[1][i]=1,s[1][i]=i;
    for (ll i=2;i<=n+1;i++)
        for (ll j=0;j<=K;j++){
            ans=0;
            for (ll sz=1;sz<i;sz++)   
                (ans+=(C[i-2][sz-1]*f[i-sz][j]%M*((s[sz][K]-s[sz][j]+M)%M)%M)%M)%=M;
        	(ans+=M)%=M;
            f[i][j]=ans;
            s[i][j]=ans;
            if (j) (s[i][j]+=s[i][j-1])%=M;
            (s[i][j]+=M)%=M;
        }
    printf("%lld\n",f[n+1][0]);
    return 0;
}