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 maxn 305
#define ll long long
using namespace std;
ll read(){
	ll x=0,c;while(!isdigit(c=getchar()));
	while(x=x*10+c-'0',isdigit(c=getchar()));
	return x;
}
ll n,k,a[maxn][maxn],f[maxn][maxn];
ll Mod;
int main(){
	n=read();k=read();Mod=read();
	for(ll i=1;i<maxn;i++)f[i][1]=1;
	for(ll i=1;i<maxn;i++)f[0][i]=1;
	a[0][0]=1;
	for(ll i=1;i<maxn;i++)
		for(ll j=0;j<=i;j++){
		a[i][j]=a[i-1][j];
		if(j)a[i][j]=(a[i][j]+a[i-1][j-1]*(i-j+1)%Mod)%Mod;
	}
	for(ll i=1;i<maxn;i++)
		for(ll j=2;j<maxn;j++)
			for(ll t=0;t<=i;t++)
				f[i][j]=(f[i][j]+f[i-t][j-1]*a[i][t])%Mod;
	printf("%lld\n",f[n][k]);
	return 0;
}