The problem can be solved recursively. If we know the position of the survivor for n-1 people, we can map it back to the circle of n people by shifting by k.

1. Base case: If n == 1, return 0 (0-indexed).
2. Recursive step: survivor_pos = (josephus(n - 1, k) + k) % n.
3. Return survivor_pos + 1 for 1-indexed result.

• Time Complexity: O(N).
• Space Complexity: O(N) (stack).

def find_the_winner(n, k):
    def solve(n, k):
        if n == 1:
            return 0
        return (solve(n - 1, k) + k) % n
        
    return solve(n, k) + 1