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 ofnums. Since the answer may be very large, return it modulo109 + 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].
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.
Input: nums = [2] Output: 0
1 <= nums.length <= 1051 <= nums[i] <= 105
implSolution{pubfnsum_subseq_widths(mutnums:Vec<i32>) -> i32{letmut x = 0;letmut pow2 = 1;letmut pow2_sum = 1;letmut ret = 0; nums.sort_unstable();for i in1..nums.len(){ x = (2* x + (nums[i] - nums[i - 1])asi64* pow2_sum) % 1_000_000_007; pow2 = (2* pow2) % 1_000_000_007; pow2_sum = (pow2_sum + pow2) % 1_000_000_007; ret = (ret + x) % 1_000_000_007;} ret asi32}}