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 <cstdio>
#include <iostream>
using namespace std;
const int Q=1<<9;
int f[Q][Q],sm[Q][Q];
int MOD;
inline int add(int a,int b)
{a+=b;return a>=MOD?a-MOD:a;}
inline int sub(int a,int b)
{a-=b;return a<0?a+MOD:a;}
inline int mul(int a,int b)
{return 1LL*a*b%MOD;}
int c[Q][Q];
int main()
{
	int n,k;
	scanf("%d%d%d",&n,&k,&MOD);
	for(int i=0;i<=n;i++){
		c[i][0]=1;
		for(int j=1;j<=i;j++)
			c[i][j]=add(c[i-1][j],c[i-1][j-1]);
	}
	for(int i=0;i<=k;i++)f[1][i]=1,sm[1][i]=k-i+1;
	for(int i=2;i<=n+1;i++){
		for(int j=0;j<=k;j++){
			for(int l=1;l<=i;l++)
				f[i][j]=add(f[i][j],mul(c[i-2][l-1],mul(f[i-l][j],sm[l][j+1])));
		}
		for(int j=k;j>=0;--j)
			sm[i][j]=add(sm[i][j+1],f[i][j]);
	}
	printf("%d",f[n+1][0]);
	return 0;
}