Fateful Chess Puzzle#1971
Profile dynamics is simple.
M. Dvorkin
In elementary school, Misha got interested in drawing, but when they moved on to drawing portraits, he started having trouble — his side-view portraits of faces always turned out jagged. That's when Misha took up chess — after all, all the lines on a chessboard are straight.
When he entered a specialized university, he started thinking about his future specialization and, since the word "profile" started to appeal to him more and more, he decided to take an in-depth approach to studies in "profile dynamics."
But it all began — including his passion for programming, as he secretly told his friends — with a simple problem that he was given to solve at the chess club for young people.
Before you proceed to tackling Misha's specialized problems, try solving this fateful little task: Find the number of ways to place rooks on an N \times N chessboard so that no two attack each other. A simple rearrangement of any rooks does not constitute a new way.
The input file contains the natural numbers and (N, K \leq 8).
Print a single integer — the answer to Misha's fateful problem.
Example 1