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# 0891. Sum of Subsequence Widths

<https://leetcode.com/problems/sum-of-subsequence-widths>

## Description

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`

## ac

```java
```