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>

const int N=305;

int n,k,mod,c[N][N],f[N][N],sum[N][N];

int main(){
	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]=(c[i-1][j-1]+c[i-1][j])%mod;
		}
	}
	for(int j=k;j>=0;--j){
		f[1][j]=1;
		sum[1][j]=(sum[1][j+1]+f[1][j])%mod;
	}
	for(int i=2;i<=n+1;++i){
		for(int j=0;j<=k;++j){
			for(int t=1;t<=i-1;++t){
				f[i][j]=(f[i][j]+1ll*c[i-2][t-1]*f[i-t][j]%mod*sum[t][j+1]%mod)%mod;
			}
		}
		for(int j=k;j>=0;--j){
			sum[i][j]=(sum[i][j+1]+f[i][j])%mod;
		}
	}
	printf("%d\n",f[n+1][0]);
	return 0;
}