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D. PolandBall and Polygon

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolandBall 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.

Input

There are only two numbers in the input: *n* and *k* (5 ≤ *n* ≤ 10^{6}, 2 ≤ *k* ≤ *n* - 2, *gcd*(*n*, *k*) = 1).

Output

You should print *n* values separated by spaces. The *i*-th value should represent number of polygon's sections after drawing first *i* lines.

Examples

Input

5 2

Output

2 3 5 8 11

Input

10 3

Output

2 3 4 6 9 12 16 21 26 31

Note

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.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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