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

Example Output

3 6 2 7 5 1 4