A bishop attacks along both diagonal directions, any distance, across an empty board. Two cells (r1, c1) and (r2, c2) (0-indexed rows and columns) are on the same diagonal if r1 + c1 == r2 + c2 (a "/"-diagonal) or r1 - c1 == r2 - c2 (a "\"-diagonal).
Given an n-by-n board and an integer k, count the number of ways to choose k cells on the board to place bishops such that no two chosen cells share either diagonal. Placements are unordered sets of cells (placing bishops at cell A and cell B is the same placement regardless of which one you "place first").
Input format
Line 1: two integers n and k.
Output format
A single integer: the number of valid placements of k non-attacking bishops.
Constraints
- 2 ≤ n ≤ 5
- 0 ≤ k ≤ 5