# K Inverse Pairs Array Problem

## Description

LeetCode Problem 629.

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:

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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:

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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

## Sample C++ Code

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const int mod = 1e9 + 7, N = 1010;

class Solution {
int f[N][N] = {};
public:
int kInversePairs(int n, int K) {
f = 1;
for (int i = 1; i <= n; ++ i) {
long long s = 0; // maintain a window that is length min(i, j);
for (int j = 0; j <= K; ++ j) {
s += f[i - 1][j];
if (j >= i)
s -= f[i - 1][j - i];
f[i][j] = ((long long)f[i][j] + s) % mod;
}
}
return f[n][K];
}
};
``````