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>
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define per(i,a,b) for(int i=(a);i>=(b);--i)
using namespace std;
const int N=305;
int n,K,P,f[N][N],sum[N][N],C[N][N];
int main(){
	cin>>n>>K>>P;
	C[0][0]=1;
	rep(i,1,N-1){
		C[i][0]=1;
		rep(j,1,i)C[i][j]=(C[i-1][j-1]+C[i-1][j])%P;
	}
	rep(i,0,K)f[1][i]=1;
	rep(i,2,n+1){
		per(j,K,0)sum[i-1][j]=(sum[i-1][j+1]+f[i-1][j])%P;
		rep(j,0,K)rep(a,1,i-1){
			f[i][j]=(f[i][j]+1LL*C[i-2][a-1]*f[i-a][j]%P*sum[a][j+1])%P;
		}
	}
	printf("%d\n",f[n+1][0]);
	return 0;
}