Incremental Partitioning Problem Statement

Given two integers N and K, determine how many ways you can partition the number N into K non-empty groups such that the size of each group[i] >= group[i-1] for each valid i. Report the result modulo 1e9 + 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 space-separated integers, N and K.

Output:

For each test case, output the number of ways modulo 1e9 + 7 on a new line.

Example:

Consider there is 1 test case and the input is:

Input:

1
5 3

Output:

2

This indicates that there are 2 ways to partition 5 into 3 groups with the specified constraints.

Constraints:

• 1 <= T <= 10
• 1 <= N <= 1000
• 1 <= K <= N

Note:

The output should be computed with a modulo of 1e9 + 7.