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Problem · Dynamic Programming

Find Arrangements

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Problem statement

Anju teaches Physics and Chemistry for P and C number of hours respectively. After teaching a particular subject for more than N number of hours continuously, Anju gets exhausted and needs to switch to another subject.

So the Principal has decided to schedule the time table for Anju in such a way that she does not teach a given subject for more than N number of hours continuously. The principal being weak in maths asks you to find out the maximum number of possible arrangements of hours in which Anju can teach a given subject for no more than N number of hours continuously.

Input format

First line contains T the required number of test cases.
Next T lines contain Three space-separated integers P, C, and N respectively.

Output format

For each test case, print the number of arrangements of hours in which Anju has not to teach a given subject for more than N number of hours continuously modulo 10^9+7.

Note: If no arrangement is possible print 0.

Function

findArrangements(P: int, C: int, N: int) → int

Examples

Example 1

P = 1C = 1N = 2return = 2

N/A

Example 2

P = 1C = 2N = 1return = 1

N/A

Constraints

1 ≤ T ≤ 100
1 ≤ P, C, N ≤ 10^3