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 to edge[i].v
#define mp make_pair
#define rint register int
#define debug(x) cerr<<#x<<"="<<x<<endl
#define fgx cerr<<"-------------"<<endl
#define N 1000
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
int c[N][N],f[N][N],s[N][N];
int main()
{	int n,K,mod; cin>>n>>K>>mod; n++;
	for(rint i=0,j;i<=n;i++)
	for(c[i][0]=1,j=1;j<=i;j++) c[i][j]=(c[i-1][j-1]+c[i-1][j])%mod;
	for(rint i=0;i<=K;i++) f[1][i]=1,s[1][i]=K-i+1;
	for(rint i=2;i<=n;i++)
	{	for(rint j=0;j<=K;j++)
		for(rint k=1;k<i;k++) f[i][j]=(f[i][j]+(ll)c[i-2][k-1]*s[k][j+1]%mod*f[i-k][j]%mod)%mod;
		for(rint j=K;j>=0;j--) s[i][j]=(s[i][j+1]+f[i][j])%mod;
	}
	cout<<f[n][0];
	return 0;
}
