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Java-based LeetCode algorithm problem solutions, regularly updated
891\. Sum of Subsequence Widths
Hard
The **width** of a sequence is the difference between the maximum and minimum elements in the sequence.
Given an array of integers `nums`, return _the sum of the **widths** of all the non-empty **subsequences** of_ `nums`. Since the answer may be very large, return it **modulo** 109 + 7.
A **subsequence** is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, `[3,6,2,7]` is a subsequence of the array `[0,3,1,6,2,2,7]`.
**Example 1:**
**Input:** nums = [2,1,3]
**Output:** 6
**Explanation:**
The subsequences are [1], [2], [3], [2,1], [2,3], [1,3], [2,1,3].
The corresponding widths are 0, 0, 0, 1, 1, 2, 2.
The sum of these widths is 6.
**Example 2:**
**Input:** nums = [2]
**Output:** 0
**Constraints:**
* 1 <= nums.length <= 105
* 1 <= nums[i] <= 105