Josephus Problem II

Consider a game where there are n children (numbered 1,2,\dots,n) in a circle. During the game, repeatedly k children are skipped and one child is removed from the circle. In which order will the children be removed?

Input

The only input line has two integers n and k.

Output

Print n integers: the removal order.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$0 \le k \le 10^9$

Example

Input

7 2

Output

3 6 2 7 5 1 4