Take-Away Game — Solution & Editorial
Positions where N is a multiple of K+1 are losing: any move leaves a non-multiple, and the opponent can always restore one. So FIRST wins iff N mod (K+1) ≠ 0.
Complexity: O(1)
Positions where N is a multiple of K+1 are losing: any move leaves a non-multiple, and the opponent can always restore one. So FIRST wins iff N mod (K+1) ≠ 0.
Complexity: O(1)