Queens

Your task is to count how many ways can you place $k$ queens on an $n \times n$ chess board so that no two queens attack each other?

You may assume that $1 \le n \le 8$ and that $1 \le k \le 3$. Your solution should be efficient in all of these cases.

In a file queens.py, implement a function count that returns the desired count.

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