{leetcode}/problems/find-the-sum-of-subsequence-powers/[LeetCode - 3098. Find the Sum of Subsequence Powers ^]
You are given an integer array nums of length n, and a positive integer k.
The power of a <span data-keyword="subsequence-array">subsequence is defined as the minimum absolute difference between any two elements in the subsequence.
Return the sum of powers of all subsequences of _`nums` which have length_ equal to k.
Since the answer may be large, return it modulo 10^9 ^+ 7.
Example 1:
<div class="example-block"> Input: <span class="example-io">nums = [1,2,3,4], k = 3
Output: <span class="example-io">4
Explanation:
There are 4 subsequences in nums which have length 3: [1,2,3], [1,3,4], [1,2,4], and [2,3,4]. The sum of powers is |2 - 3| + |3 - 4| + |2 - 1| + |3 - 4| = 4.
Example 2:
<div class="example-block"> Input: <span class="example-io">nums = [2,2], k = 2
Output: <span class="example-io">0
Explanation:
The only subsequence in nums which has length 2 is [2,2]. The sum of powers is |2 - 2| = 0.
Example 3:
<div class="example-block"> Input: <span class="example-io">nums = [4,3,-1], k = 2
Output: <span class="example-io">10
Explanation:
There are 3 subsequences in nums which have length 2: [4,3], [4,-1], and [3,-1]. The sum of powers is |4 - 3| + |4 - (-1)| + |3 - (-1)| = 10.
Constraints:
-
2 ⇐ n == nums.length ⇐ 50 -
`-108 ⇐ nums[i] ⇐ 108 `
-
2 ⇐ k ⇐ n