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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 ith
and jth
element in the array, if 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 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 pair.
Example 2:
Input: n = 3, k = 1
Output: 2
Explanation:
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].
[Dynamic Programming]