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1818\. Minimum Absolute Sum Difference

Medium

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

The **absolute sum difference** of arrays `nums1` and `nums2` is defined as the **sum** of `|nums1[i] - nums2[i]|` for each `0 <= i < n` (**0-indexed**).

You can replace **at most one** element of `nums1` with **any** other element in `nums1` to **minimize** the absolute sum difference.

Return the _minimum absolute sum difference **after** replacing at most one element in the array `nums1`._ Since the answer may be large, return it **modulo** 10⁹ + 7.

`|x|` is defined as:

*   `x` if `x >= 0`, or
*   `-x` if `x < 0`.

**Example 1:**

**Input:** nums1 = [1,7,5], nums2 = [2,3,5]

**Output:** 3

**Explanation:** There are two possible optimal solutions: 

- Replace the second element with the first: [1,**7**,5] => [1,**1**,5], or 

- Replace the second element with the third: [1,**7**,5] => [1,**5**,5]. 
  
Both will yield an absolute sum difference of `|1-2| + (|1-3| or |5-3|) + |5-5| =` 3\.

**Example 2:**

**Input:** nums1 = [2,4,6,8,10], nums2 = [2,4,6,8,10]

**Output:** 0

**Explanation:** nums1 is equal to nums2 so no replacement is needed. This will result in an absolute sum difference of 0.

**Example 3:**

**Input:** nums1 = [1,10,4,4,2,7], nums2 = [9,3,5,1,7,4]

**Output:** 20

**Explanation:** Replace the first element with the second: [**1**,10,4,4,2,7] => [**10**,10,4,4,2,7]. This yields an absolute sum difference of `|10-9| + |10-3| + |4-5| + |4-1| + |2-7| + |7-4| = 20`

**Constraints:**

*   `n == nums1.length`
*   `n == nums2.length`
*   1 <= n <= 10⁵
*   1 <= nums1[i], nums2[i] <= 10⁵