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 ll long long
using namespace std;
template<typename tn> void read(tn &a){
	tn x=0,f=1; char c=' ';
	for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-'0';
	a=x*f;
}
const int N = 510;
int f[N][N],g[N][N],n,K,mod,C[N][N];
int main(){
	read(n);read(K);read(mod);
	for(int i=0;i<=n;i++){
		C[i][0]=1;
		for(int j=1;j<=i;j++)
			C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
	}
	for(int i=0;i<=K;i++) f[1][i]=1,g[1][i]=K-i+1;
	for(int i=2;i<=n+1;i++)
		for(int j=K;~j;j--){
			ll res=0;
			for(int p=1;p<i;p++)
				res=(res+1ll*g[p][j+1]*f[i-p][j]%mod*C[i-2][p-1])%mod;
			f[i][j]=res;
			g[i][j]=(res+g[i][j+1])%mod;
		}
	cout<<f[n+1][0]<<'\n';
	return 0;
}
