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=307;
int P,C[N][N],f[N][N],s[N][N];
void inc(int&a,int b){a+=b-P,a+=a>>31&P;}
void dec(int&a,int b){a-=b,a+=a>>31&P;}
int main()
{
    int n,k;scanf("%d%d%d",&n,&k,&P);
    for(int i=0;i<=n;++i) for(int j=C[i][0]=1;j<=i;++j) inc(C[i][j]=C[i-1][j],C[i-1][j-1]);
    for(int i=0;i<=k;++i) f[1][i]=1,s[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) inc(f[i][j],1ll*f[i-l][j]*s[l][j+1]%P*C[i-2][l-1]%P);
	for(int j=k;j;--j) inc(s[i][j]=s[i][j+1],f[i][j]);
    }
    printf("%d",f[n+1][0]);
}
