Given an array, an inversion is defined as a pair a[i], a[j] such that a[i] > a[j] and i < j. Given two numbers N and K, the task is to find the count of the number of permutations of first N numbers have exactly K inversion.

Note: Answer can be large, output answer modulo 10^{9} + 7

Example 1:

Input: N = 3, K = 1
Output: 2Explanation: Total Permutation of first
3 numbers, 123, 132, 213, 231, 312, 321
Permutation with 1 inversion : 132 and 213

Example 2:

Input: N = 3, K = 3
Output: 0Explanation: No such permutation

Your Task:
You don't need to read input or print anything. Complete the function numberOfPermWithKInversion() which takes N and K as input parameters and returns the integer value

Expected Time Complexity: O(N*K) Expected Auxiliary Space: O(N*K)