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;
typedef long long ll;
const int N=305;
int read(){
	int f=1,g=0;
	char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-1;
	for (;isdigit(ch);ch=getchar()) g=g*10+ch-'0';
	return f*g;
}
int n,K,p,C[N][N],f[N][N],s[N][N];
void check(int &x,int y){if ((x+=y)>=p) x-=p;}
int pl(int x,int y){if ((x+=y)>=p) x-=p;return x;}

int main(){
	n=read();K=read();p=read();
	for (int i=0;i<=n;i++){
		C[i][0]=1;
		for (int j=1;j<=i;j++) C[i][j]=pl(C[i-1][j],C[i-1][j-1]);
	}
	for (int i=K;i>=0;i--){f[1][i]=1;s[1][i]=pl(f[1][i],s[1][i+1]);}
	for (int i=2;i<=n+1;i++)
	for (int j=K;j>=0;j--){
		for (int k=1;k<i;k++)
		check(f[i][j],(ll)f[i-k][j]*C[i-2][k-1]%p*s[k][j+1]%p);
		s[i][j]=pl(f[i][j],s[i][j+1]);
	}
	printf("%d\n",f[n+1][0]);
	return 0;
}