<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:
    def sumSubseqWidths(self, nums: List[int]) -> int:
        N = len(nums)
        nums.sort()
        MOD = 10 ** 9 + 7
        delta = 0
        cur_subseq_count = 1
        total = 0


        for i in range(1, N):
            delta += (nums[i] - nums[i - 1]) * cur_subseq_count
            delta %= MOD

            total = 2 * total + delta
            total %= MOD

            cur_subseq_count += pow(2, i, MOD)
            cur_subseq_count %= MOD






        
        return total
        
29600