P9645 [SNCPC2019] K-hour Clock

A $k$-hour clock is a day keeping method which follows the rules below: - A day is divided into $k$ hours, where the $i$-th hour is called the $(i-1)$ o' clock; - If it's $x$ o'clock now, it will be $(x+1)$ o'clock after $1$ hour if $0 \le x < k - 1$; - If it's $(k - 1)$ o'clock now, it will be $0$ o'clock after $1$ hour. We know that it's $x$ o'clock now, and after $y$ hours it will be $z$ o'clock. What's the value of $k$?

There are multiple test cases. The first line of the input is an integer $T$ (about $10^5$), indicating the number of test cases. For each test case: The first and only line contains three integers $x$, $y$ and $z$ ($0 \le x, z \le 10^9$, $1 \le y \le 10^9$).

For each test case output one line containing one integer, indicating the value of $k$. Note that there must be $1 \le k \le 2 \times 10^9$. If there are multiple valid answers, you can print any of them; If there is no valid answer, print ``-1`` (without quotes) instead.