CF2180A Carnival Wheel

You have a prize wheel divided into $ l $ sections, numbered from $ 0 $ to $ l-1 $ . The sections are arranged in a circle, so after section $ l-1 $ , the numbering continues again from section $ 0 $ . Initially, the prize pointer is at section $ a $ . Each time you spin the wheel, the pointer moves exactly $ b $ sections forward. That is, after one spin, the pointer moves from section $ a $ to section $ (a+b)\bmod l $ , after two spins to $ (a+2b)\bmod l $ , and so on $ ^{\text{∗}} $ . You may spin the wheel any number of times (including zero). After you stop, the section where the pointer finally lands determines your prize: you receive an amount equal to the number of that section. What is the maximum prize you can obtain? $ ^{\text{∗}} $ Here, $ x \bmod y $ denotes the remainder from dividing $ x $ by $ y $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 500 $ ). The description of the test cases follows. The first line of each test case contains three integers $ l, a $ , and $ b $ ( $ 1 \le l, b \le 5000 $ , $ 0 \le a \le l-1 $ ).

For each test case, output the maximum prize that can be obtained.

In the first test case, by spinning the wheel three times and then claiming the reward, you can obtain a maximum value of $ 4 $ . The sequence of pointer positions is: $ 3, 0, 2, 4, 1, 3, 0, \ldots $ In the second test case, the pointer will remain on section $ 0 $ indefinitely. In the fourth test case, with $ b = 1 $ and starting from section $ 0 $ , the pointer will iterate over all sections, including the last one. [Link to the visualizer](https://codeforces.com/assets/contests/2180/A_uegoe0Taex5phi0Ieni9.html)