Problem Statement

You are given integers $N$ and $K$.

Let's call an integer array a=\[a_1, a_2, \\ldots, a_K\] of length $K$ good, if $1 \\le a_i \\le i$ for all $1 \\le i \\le K$.

Let's call an integer array b=\[b_1, b_2, \\ldots, b_{NK}\] of length $NK$ amazing, if it can be split into $N$ (not necessarily contiguous) subsequences of length $K$, each of which is good.

Let's define $f(pos, val)$ as the number of amazing sequences $b$ such that $b_{pos}=val$.

Find $f(pos, val)$ for all $1\\le pos \\le NK$, $1 \\le val \\le K$. As these numbers can be very big, output them modulo some prime $P$.

Constraints

• $1 \\le N \\le 20$.
• $1 \\le K \\le 20$.
• $10^8 \\le P \\le 10^9$
• $P$ is a prime.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $P$

Output

Output $NK$ lines. The $j$-th number in the $i$-th line should be equal to $(f(i, j) \\bmod P)$.

Sample Input 1

2 2 965166677

Sample Output 1

6 0 
4 2 
4 2 
3 3 

There exist $6$ amazing arrays:

• \[1, 1, 1, 1\] ー can be split into \[b_1, b_2\], \[b_3, b_4\].
• \[1, 1, 1, 2\] ー can be split into \[b_1, b_2\], \[b_3, b_4\].
• \[1, 2, 1, 1\] ー can be split into \[b_1, b_2\], \[b_3, b_4\].
• \[1, 2, 1, 2\] ー can be split into \[b_1, b_2\], \[b_3, b_4\].
• \[1, 1, 2, 1\] ー can be split into \[b_1, b_3\], \[b_2, b_4\].
• \[1, 1, 2, 2\] ー can be split into \[b_1, b_3\], \[b_2, b_4\].