0629. K Inverse Pairs Array

https://leetcode.com/problems/k-inverse-pairs-array

Description

For an integer array nums, an inverse pair is a pair of integers [i, j] where 0 <= i < j < nums.length and nums[i] > nums[j].

Given two integers n and k, return the number of different arrays consist of numbers from 1 to n such that there are exactly k inverse pairs. Since the answer can be huge, return it modulo 109 + 7.

Example 1:

**Input:** n = 3, k = 0
**Output:** 1
**Explanation:** Only the array [1,2,3] which consists of numbers from 1 to 3 has exactly 0 inverse pairs.

Example 2:

**Input:** n = 3, k = 1
**Output:** 2
**Explanation:** The array [1,3,2] and [2,1,3] have exactly 1 inverse pair.

Constraints:

• 1 <= n <= 1000

• 0 <= k <= 1000

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