Your task is to calculate how many ways k queens can be placed on an n $\backslash$times n chessboard such that no two queens threaten each other.

You can assume that $1<=$ n $<=8$ and $1<=$ k $<=3.$ Your solution should efficiently handle all these cases

do you know how i can solve the problem using python code?

Implement a function count in the phyton file to compute the resulto you know how i can solve the problem using python code?

def count$($n$,$ k$)$:

# TODO

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

print$($count$(2,1))$ # $4$

print$($count$(2,2))$ # $0$

print$($count$(5,3))$ # $204$

print$($count$(7,1))$ # $49$

print$($count$(7,2))$ # $700$

print$($count$(7,3))$ # $3628$