Python3: Simulate + adjust index for modulo
IntuitionApproachComplexity

Time complexity: O(n)


Space complexity: O(n) (using set)

Code
# Intuition
<!-- Describe your first thoughts on how to solve this problem. -->

# Approach
<!-- Describe your approach to solving the problem. -->

# Complexity
- Time complexity: O(n)

- Space complexity: O(n) (using set)
<!-- Add your space complexity here, e.g. $$O(n)$$ -->

# Code
```python3 []
class Solution:
    def circularGameLosers(self, n: int, k: int) -> List[int]:
        # Base Case: 1st friend wins
        if k == n:
            return list(range(2,n+1))
        frens = set() # Contain winners
        count = 1
        i = 1 # First friend
        while i not in frens:
            frens.add(i)

            steps = count * k
            # Adjust 1-indexed frens to 0 for modulo
            adjust_frens = (i + steps - 1) 
            # Adjust back to 1-indexed
            i = (adjust_frens % n) + 1 # Forward circular

            count += 1
        
        # Extract losers
        losers = [i for i in range(1, n+1) if i not in frens]
        return losers

```
['Python3']