Josephus Problem 3

The Josephus problem is as follows.

$N$ people numbered 1 to $N$ sit in a circle, and a positive integer $K$ ($K \le N$) is given. Counting in order, every $K$-th person is removed. Once a person is removed, the counting continues around the circle formed by the remaining people. The process runs until all $N$ people are removed, and the order in which people are removed is the $(N, K)$-Josephus permutation. For example, the $(7, 3)$-Josephus permutation is <3, 6, 2, 7, 5, 1, 4>.

Given $N$ and $K$, write a program that finds the number of the person who remains last.

The first line contains $N$ and $K$ in that order, separated by a space. ($1 \le K \le N \le 5{,}000{,}000$)

Print the number of the person who remains last on the first line.