You are given a $0$ indexed integer array nums and an integer k.

In one operation, you can choose any index i and either increment or decrement nums[i] by $1$.

The array nums is called modulo alternating if there exist two distinct integers x and y such that:

• $0 \leq$ x, y $< k$

• x $\neq$ y

• nums[i] % k == x for all even indices i

• nums[i] % k == y for all odd indices i

Return the minimum number of operations needed to make nums modulo alternating.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $2 \leq$ k $\leq 10^5$

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.