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
//I love Nnanami Chiaki
#include<bits/stdc++.h>
using namespace std;
const int maxn=307;
int n,k,m;
int dp[maxn][maxn],sum[maxn][maxn],c[maxn][maxn];
void init(){
	c[0][0]=1;
	for (int i=1;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])%m;
	}
}
int main(){
	scanf("%d%d%d",&n,&k,&m);
	init();
	for (int i=k;i>=0;i--) dp[1][i]=1;
	for (int i=k;i>=0;i--) sum[1][i]=(sum[1][i+1]+dp[1][i])%m;
	for (int i=2;i<=n+1;i++){
		for (int j=0;j<=k;j++){
			for (int sz=1;sz<i;sz++) dp[i][j]=(dp[i][j]+1ll*dp[i-sz][j]*c[i-2][sz-1]%m*sum[sz][j+1]%m)%m;
		}
		for (int j=k;j>=0;j--) sum[i][j]=(sum[i][j+1]+dp[i][j])%m;
	}
	printf("%d\n",dp[n+1][0]);
	return 0;
} 