Return top-k subset sums in descending order

Problem

You are given n distinct objects, each with a non-negative integer weight. A subset can be any selection of these objects (including the empty subset).

Define the weight of a subset as the sum of weights of the objects in that subset.

Task

Return the k subset weights with the largest sums, sorted in descending order.

Input

• An integer array w of length n ( w[i] >= 0 ), where all objects are distinct.
• An integer k .

Output

• A list/array of length k containing the k largest subset sums in non-increasing order.

Notes / Clarifications

• Different subsets may have the same sum; treat them as separate results if they correspond to different subsets.
• You may assume 1 <= k <= 2^n .

Example

If w = [3, 2, 1]:

• Subset sums are: 0, 1, 2, 3, 3, 4, 5, 6
• The top k=4 sums (descending) are: [6, 5, 4, 3]

Constraints (typical interview-style)

• 1 <= n <= 2e5 (or large enough that enumerating all 2^n subsets is infeasible)
• 0 <= w[i] <= 1e9
• 1 <= k <= min(2^n, 2e5)