What is the minimum number of increment or decrement operations needed to ensure that all subarrays of length k have the same sum?

edit

The minimum number of increment or decrement operations needed to ensure that all subarrays of length k have the same sum is 0 or 1.

If all subarrays of length k already have the same sum, then no operations are needed and the answer is 0.

If there is a subarray of length k whose sum is different from the sum of the other subarrays of length k, then we can increment or decrement a single element of that subarray to make its sum equal to the sum of the other subarrays. Therefore, we only need to perform one operation to achieve this.

Note that if there are multiple subarrays with different sums, we can choose any of them to increment or decrement a single element, and the result will still be valid.