Josephus Problem II

Consider a game where there are $nn$ children (numbered $1,2,\dots ,n1,2,\backslash dots,n$) in a circle. During the game, repeatedly $kk$ 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 $nn$ and $kk$.

Output

Print $nn$ integers: the removal order.