Given two integers n and k, construct a list ans containing $n$ integers such that:

• ans is a permutation of all integers from $1$ to $n$.

• The list of adjacent absolute differences $[|`ans`[0] - `ans`[1]|, |`ans`[1] - `ans`[2]|, \dots, |`ans`[n - 2] - `ans`[n - 1]|]$ contains exactly $k$ distinct values.

Return the list ans. If there are multiple valid answers, return any of them.

Constraints:

• $1 \leq `k` < `n` \leq 10^4$

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.