3428 - Maximum and Minimum Sums of at Most Size K Subsequences.

Medium

You are given an integer array nums and a positive integer k. Return the sum of the maximum and minimum elements of all

subsequences

of nums with at most k elements.

Since the answer may be very large, return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: nums = 1,2,3, k = 2

Output: 24

Explanation:

The subsequences of nums with at most 2 elements are:

The output would be 24.

Example 2:

Input: nums = 5,0,6, k = 1

Output: 22

Explanation:

For subsequences with exactly 1 element, the minimum and maximum values are the element itself. Therefore, the total is 5 + 5 + 0 + 0 + 6 + 6 = 22.

Example 3:

Input: nums = 1,1,1, k = 2

Output: 12

Explanation:

The subsequences [1, 1] and [1] each appear 3 times. For all of them, the minimum and maximum are both 1. Thus, the total is 12.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁹</code>

• 1 <= k <= min(70, nums.length)