There are n friends standing in a circle, numbered clockwise from $1$ to n.

The game starts with friend $1$ holding the ball. The game proceeds in steps:

• In the $i^{ ext{th}}$ step (starting at $i = 1$), the friend currently holding the ball passes it to the friend who is $i imes$ k positions ahead in the clockwise direction.

• The game concludes immediately when any friend receives the ball for the $2^{ ext{nd}}$ time.

The losers of the game are the friends who never touched the ball.

Return an array containing the numbers of the losers, sorted in ascending order.

Constraints:

• $1 \leq$ k $\leq$ n $\leq 50$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.