Josephus Problem II

• Time limit: 1.00 s
• Memory limit: 512 MB

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