josephus-problem.js

# Josephus Problem

Josephus problem is a math puzzle with a grim description:  `n`  prisoners are standing on a circle, sequentially numbered from  `1`  to  `n−1`.

An executioner walks along the circle, starting from prisoner  0 , removing every  k -th prisoner and killing him.

As the process goes on, the circle becomes smaller and smaller, until only one prisoner remains, who is then freed.

For example, if there are `n=5` prisoners and `k=2`, the order the prisoners are killed in (let's call it the "killing sequence") will be 2, 4, 1, and 5, and the survivor will be #3.

Given any `n,k>0`, find out which prisoner will be the final survivor.

For example, there were 41 prisoners and every 3rd prisoner was being killed (`k=3`).

Among them was a clever chap name Josephus who worked out the problem, stood at the surviving position, and lived on to tell the tale.

Which number was he?

`josephus(5,3)` should return `3`.
`josephus(6,2)` should return `5`.
`josephus(7,2)` should return `7`.
`josephus(8,2)` should return `1`.