2333 - Minimum Sum of Squared Difference\.

Medium

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 <code>(nums1i - nums2i)²</code> 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.

Note: You are allowed to modify the array elements to become negative integers.

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 nums10 once.

• Increase nums22 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

• <code>1 <= n <= 10⁵</code>

• <code>0 <= nums1i, nums2i<= 10⁵</code>

• <code>0 <= k1, k2 <= 10⁹</code>