<p>The <strong>width</strong> of a sequence is the difference between the maximum and minimum elements in the sequence.</p>

<p>Given an array of integers <code>nums</code>, return <em>the sum of the <strong>widths</strong> of all the non-empty <strong>subsequences</strong> of </em><code>nums</code>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>A <strong>subsequence</strong> 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, <code>[3,6,2,7]</code> is a subsequence of the array <code>[0,3,1,6,2,2,7]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,1,3]
<strong>Output:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [2]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    /*
    
    (nums[0] * 1 + nums[1] * 2 + nums[2] * 4)
    - (nums[2] * 1 + nums[1] * 2 + nums[0] * 4)

    % 1e9 + 7
    
    */
    static constexpr int mod = 1e9 + 7;

    int sumSubseqWidths(vector<int>& nums) {
        ranges::sort(nums);

        int64_t res = 0;
        for (int i = 0, m = 1; i < nums.size(); ++i, m = m * 2 % mod) {
            int64_t add = int64_t(nums[i]) * m - int64_t(nums[nums.size()-i-1]) * m;
            res = (res + add) % mod;
        }
        
        return res;
    }
};
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