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<cstring>
#include<cmath>
#include<iostream>
using namespace std;
#define N 360
#define int long long
int c[N][N],t[N],f[N],n,k,m;
void exp(int *a){
	memcpy(t,a,sizeof(t));
	for(int i=0;i<=n;i++)
		for(int j=0;j<i;j++)
			a[i]=(a[i]+t[j]*a[i-j-1]%m*c[i][j])%m;
}
signed main(){
	cin>>n>>k>>m;
	c[0][0]=1;
	for(int i=1;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])%m;
	}
	n++;
	for(int i=0;i<n;i++)
		f[i]=1;
	k--;
	for(int i=1;i<=k;i++)
		exp(f);
	n--;
	cout<<f[n];
}