Find Arrangements

Problem Overview

• Compute the number of valid schedules arranging P hours of Physics and C hours of Chemistry so no subject exceeds N consecutive hours.
• Input: T test cases with integers P, C, N. Output: count of arrangements modulo 1e9+7; print 0 if none.
• Constraints: 1 ≤ T ≤ 100; 1 ≤ P, C, N ≤ 10^3.
• Context: school timetable planning to limit continuous teaching and reduce fatigue.
• From IBM interviews; a coding interview problem and interview question.