Find the Winner of the Circular Game

lcpy gen -n 1823   # by problem number
lcpy gen -s find_the_winner_of_the_circular_game   # by problem name

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.

class Solution:
    # Time: O(n)
    # Space: O(1)
    def find_the_winner(self, n: int, k: int) -> int:
        # Josephus recurrence on 0-indexed survivors:
        # with `size` friends left, the survivor sits (k % size) positions
        # clockwise after the survivor of the `size - 1` round.
        winner = 0
        for size in range(2, n + 1):
            winner = (winner + k) % size
        return winner + 1