--description--

Josephus problem is a math puzzle with a grim description: $n$ prisoners are standing on a circle, sequentially numbered from $0$ 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 1, 3, 0, and 4, and the survivor will be #2.

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

In one such incident, there were 41 prisoners and every 3^rd 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?

--instructions--

Write a function that takes the initial number of prisoners and k as parameters and returns the number of the prisoner that survives.

--hints--

josephus should be a function.

assert(typeof josephus == 'function');

josephus(30,3) should return a number.

assert(typeof josephus(30, 3) == 'number');

josephus(30,3) should return 28.

assert.equal(josephus(30, 3), 28);

josephus(30,5) should return 2.

assert.equal(josephus(30, 5), 2);

josephus(20,2) should return 8.

assert.equal(josephus(20, 2), 8);

josephus(17,6) should return 1.

assert.equal(josephus(17, 6), 1);

josephus(29,4) should return 1.

assert.equal(josephus(29, 4), 1);

--seed--

--seed-contents--

function josephus(init, kill) {

}

--solutions--

function josephus(init, kill) {
  const arr = Array.from(Array(init).keys());
  let curr = -1
  while (arr.length > 1) {
    curr = (curr + kill) % arr.length;
    arr.splice(curr, 1);
    curr--;
  }
  return arr[0];
}