Non-attacking Kings Placement

Given an \(N \times N\) chessboard, the task is to place \(K\) kings such that no two kings attack each other. A king can attack one square in each of the eight directions: up, down, left, right, and the four diagonals. In other words, if a king is placed at cell \((i,j)\), it can attack any cell \((i+dx, j+dy)\) for \(dx,dy \in \{-1,0,1\}\) (except when both are zero). The goal is to count the number of distinct arrangements for placing the kings.

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inputFormat

The input consists of two space-separated integers: \(N\) and \(K\), where \(N\) represents the size of the chessboard (i.e. the board is \(N \times N\)) and \(K\) is the number of kings to place.

outputFormat

Output a single integer, which is the number of valid arrangements to place \(K\) non-attacking kings on an \(N \times N\) chessboard.

sample

1 1

1