CF755D PolandBall and Polygon

PolandBall has such a convex polygon with $ n $ veritces that no three of its diagonals intersect at the same point. PolandBall decided to improve it and draw some red segments. He chose a number $ k $ such that $ gcd(n,k)=1 $ . Vertices of the polygon are numbered from $ 1 $ to $ n $ in a clockwise way. PolandBall repeats the following process $ n $ times, starting from the vertex $ 1 $ : Assume you've ended last operation in vertex $ x $ (consider $ x=1 $ if it is the first operation). Draw a new segment from vertex $ x $ to $ k $ -th next vertex in clockwise direction. This is a vertex $ x+k $ or $ x+k-n $ depending on which of these is a valid index of polygon's vertex. Your task is to calculate number of polygon's sections after each drawing. A section is a clear area inside the polygon bounded with drawn diagonals or the polygon's sides.

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The greatest common divisor (gcd) of two integers $ a $ and $ b $ is the largest positive integer that divides both $ a $ and $ b $ without a remainder. For the first sample testcase, you should output "2 3 5 8 11". Pictures below correspond to situations after drawing lines.