Ninja and the New Year Guests Problem

Ninja has organized a new year party and wants to verify if the guests are programmers by challenging them with a coding task. As an invited programmer, you're tasked to solve it.

You need to compute the number of permutations of integers from 0 to N-1 such that at least K positions in the permutation satisfy ARR[I] = I (where 0 ≤ I < N).

The result should be given modulo 10⁹ + 7.

Input:

The first line contains an integer 'T', indicating the number of test cases.
Each test case consists of a single line with two integers 'N' and 'K'.

Output:

For each test case, print the number of valid permutations modulo 10^9 + 7.

Example:

Input:

'N' = 4 'K' = 3

Output:

1

Explanation: There is only one permutation [0, 1, 2, 3] such that the number of elements satisfying ARR[I] = I is K = 3.

Constraints:

• 1 ≤ 'T' ≤ 10^4
• 4 ≤ 'N' ≤ 10^18
• 'N - 4' ≤ 'K' ≤ 'N'
• 1 ≤ K
• Time Limit: 1 second

Note:

You do not need to print anything. Just implement the provided function.