n friends that are playing a game. The friends are sitting in a circle and are numbered from
n in clockwise order. More formally, moving clockwise from the
ith friend brings you to the
(i+1)th friend for
1 <= i < n, and moving clockwise from the
nth friend brings you to the
The rules of the game are as follows:
kfriends in the clockwise direction including the friend you started at. The counting wraps around the circle and may count some friends more than once.
2starting from the friend immediately clockwise of the friend who just lost and repeat.
Given the number of friends,
n, and an integer
k, return the winner of the game.
Input: n = 5, k = 2 Output: 3 Explanation: Here are the steps of the game: 1) Start at friend 1. 2) Count 2 friends clockwise, which are friends 1 and 2. 3) Friend 2 leaves the circle. Next start is friend 3. 4) Count 2 friends clockwise, which are friends 3 and 4. 5) Friend 4 leaves the circle. Next start is friend 5. 6) Count 2 friends clockwise, which are friends 5 and 1. 7) Friend 1 leaves the circle. Next start is friend 3. 8) Count 2 friends clockwise, which are friends 3 and 5. 9) Friend 5 leaves the circle. Only friend 3 is left, so they are the winner.
Input: n = 6, k = 5 Output: 1 Explanation: The friends leave in this order: 5, 4, 6, 2, 3. The winner is friend 1.
1 <= k <= n <= 500
Could you solve this problem in linear time with constant space?