Minimum Sum of Squared Difference

You are given two positive 0-indexed integer arrays nums1 and nums2, both of length n.

The sum of squared difference of arrays nums1 and nums2 is defined as the sum of (nums1[i] - nums2[i])^2 for each 0 <= i < n.

You are also given two positive integers k1 and k2. You can modify any of the elements of nums1 by +1 or -1 at most k1 times. Similarly, you can modify any of the elements of nums2 by +1 or -1 at most k2 times.

Return the minimum sum of squared difference after modifying array nums1 at most k1 times and modifying array nums2 at most k2 times.

Example 1:

Input: nums1 = [1,2,3,4], nums2 = [2,10,20,19], k1 = 0, k2 = 0

Output: 579

Explanation: The elements in nums1 and nums2 cannot be modified because k1 = 0 and k2 = 0. The sum of square difference will be: (1 - 2)^2 + (2 - 10)^2 + (3 - 20)^2 + (4 - 19)^2 = 579.

Example 2:

Input: nums1 = [1,4,10,12], nums2 = [5,8,6,9], k1 = 1, k2 = 1

Output: 43

Explanation: One way to obtain the minimum sum of square difference is:

• Increase nums1[0] once.
• Increase nums2[2] once.

The minimum of the sum of square difference will be: (2 - 5)^2 + (4 - 8)^2 + (10 - 7)^2 + (12 - 9)^2 = 43. Note that there are other ways to obtain the minimum of the sum of square difference, but there is no way to obtain a sum smaller than 43.

Constraints:

• n == nums1.length == nums2.length
• 1 <= n <= 100,000
• 0 <= nums1[i], nums2[i] <= 100,000
• 0 <= k1, k2 <= 1,000,000,000