Q. Josephus Problem II
time limit per test
2 s
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$k$$$.

Constraints:

  • $$$1 \le n \le 2\cdot 10^5$$$
  • $$$1 \le k \le 10^9$$$
Output

Print $$$n$$$ integers: the removal order.

Example
Input
7 2
Output
3 6 2 7 5 1 4