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Given two integers `n`

and `k`

, find how many different arrays consist of numbers from `1`

to `n`

such that there are exactly `k`

inverse pairs.

We define an inverse pair as following: For `i`

and _{th}`j`

element in the array, if _{th}`i`

< `j`

and `a[i]`

> `a[j]`

then it's an inverse pair; Otherwise, it's not.

Since the answer may be very large, the answer should be 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 pair.

**Example 2:**

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

**Note:**

- The integer
`n`

is in the range [1, 1000] and`k`

is in the range [0, 1000].