{"raw_statement":[{"iden":"statement","content":"A $k$-hour clock is a day keeping method which follows the rules below:\n\n- A day is divided into $k$ hours, where the $i$-th hour is called the $(i-1)$ o' clock;\n- If it's $x$ o'clock now, it will be $(x+1)$ o'clock after $1$ hour if $0 \\le x < k - 1$;\n- If it's $(k - 1)$ o'clock now, it will be $0$ o'clock after $1$ hour.\n\nWe know that it's $x$ o'clock now, and after $y$ hours it will be $z$ o'clock. What's the value of $k$?\n"},{"iden":"input","content":"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:\n\nThe first and only line contains three integers $x$, $y$ and $z$ ($0 \\le x, z \\le 10^9$, $1 \\le y \\le 10^9$)."},{"iden":"output","content":"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."}],"translated_statement":null,"sample_group":[["4\n11 18 5\n3 49 4\n1 9 1\n1 3 10","12\n24\n3\n-1"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}