629. K Inverse Pairs Array

Hard

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218

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** `10`

.^{9} + 7

**Example 1:**

Input:n = 3, k = 0Output:1Explanation: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 = 1Output:2Explanation: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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