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# 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`

## ac

```java
```