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Integer Partition

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1193    Accepted Submission(s): 638


Problem Description
Given n, k, calculate the number of different (unordered) partitions of n such that no part is repeated k or more times.
 

Input
First line, number of test cases, T.
Following are T lines. Each line contains two numbers, n and k.

1<=n,k,T<=105
 

Output
T lines, each line contains answer to the responding test case.
Since the numbers can be very large, you should output them modulo 109+7.
 

Sample Input
4
4 2
4 3
4 4
4 5
 

Sample Output
2
4
4
5
 

Source
2013 Multi-University Training Contest 6
 

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