1823 - Find the Winner of the Circular Game.

Medium

There are n friends that are playing a game. The friends are sitting in a circle and are numbered from 1 to n in clockwise order. More formally, moving clockwise from the <code>i^th</code> friend brings you to the <code>(i+1)^th</code> friend for 1 <= i < n, and moving clockwise from the <code>n^th</code> friend brings you to the <code>1^st</code> friend.

The rules of the game are as follows:

• Start at the <code>1^st</code> friend.

• Count the next k friends in the clockwise direction including the friend you started at. The counting wraps around the circle and may count some friends more than once.

• The last friend you counted leaves the circle and loses the game.

• If there is still more than one friend in the circle, go back to step 2 starting from the friend immediately clockwise of the friend who just lost and repeat.

• Else, the last friend in the circle wins the game.

Given the number of friends, n, and an integer k, return the winner of the game.

Example 1:

Input: n = 5, k = 2

Output: 3

Explanation: Here are the steps of the game:

• Start at friend 1.

• Count 2 friends clockwise, which are friends 1 and 2.

• Friend 2 leaves the circle. Next start is friend 3.

• Count 2 friends clockwise, which are friends 3 and 4.

• Friend 4 leaves the circle. Next start is friend 5.

• Count 2 friends clockwise, which are friends 5 and 1.

• Friend 1 leaves the circle. Next start is friend 3.

• Count 2 friends clockwise, which are friends 3 and 5.

• Friend 5 leaves the circle. Only friend 3 is left, so they are the winner.

Example 2:

Input: n = 6, k = 5

Output: 1

Explanation: The friends leave in this order: 5, 4, 6, 2, 3. The winner is friend 1.

Constraints:

• 1 <= k <= n <= 500