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;
int n,mo,k,c[500][500],f[500][500],w[500][500];
int main(){
    scanf("%d%d%d",&n,&k,&mo);
    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-1]+c[i-1][j])%mo;
    }
    for(int i=k;i>=0;--i){
		f[i][0]=1;
		for(int j=1;j<=n;++j)
	    for (int t=0;t<j;++t)
		(f[i][j]+=1ll*w[i+1][j-t-1]*f[i][t]%mo*c[j-1][t]%mo)%=mo;
	for (int j=0;j<=n;++j)
	    w[i][j]=(w[i+1][j]+f[i][j])%mo;
    }
    cout<<f[0][n];
    return 0;
}