Who's Opposite?

题意翻译

有 $n$ 个人围成一个环站立，它们按照顺时针顺序编号为 $1$ 到 $n$。每个人都与唯一对应的另外一个人互相对视。 现在，我们不给你环的人数，而是告诉你三个数 $a,b,c$。你需要回答：如果在一个环中，编号为 $a$ 和 $b$ 的人互相对视，那么是否存在这样的环？如果存在，请求出在这个环中与编号为 $c$ 的人互相对视的人的编号。如果不存在请输出 `-1`。 $t$ 组数据，$1\leqslant t\leqslant 10^4$，$1\leqslant a,b,c\leqslant 10^8$。 Translated by Eason_AC 2021.8.19

题目描述

Some number of people (this number is even) have stood in a circle. The people stand in the circle evenly. They are numbered clockwise starting from a person with the number $ 1 $ . Each person is looking through the circle's center at the opposite person. A sample of a circle of $ 6 $ persons. The orange arrows indicate who is looking at whom.You don't know the exact number of people standing in the circle (but this number is even, no doubt). It is known that the person with the number $ a $ is looking at the person with the number $ b $ (and vice versa, of course). What is the number associated with a person being looked at by the person with the number $ c $ ? If, for the specified $ a $ , $ b $ , and $ c $ , no such circle exists, output -1.

输入输出格式

输入格式

The first line contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Then $ t $ test cases follow. Each test case consists of one line containing three distinct integers $ a $ , $ b $ , $ c $ ( $ 1 \le a,b,c \le 10^8 $ ).

输出格式

For each test case output in a separate line a single integer $ d $ — the number of the person being looked at by the person with the number $ c $ in a circle such that the person with the number $ a $ is looking at the person with the number $ b $ . If there are multiple solutions, print any of them. Output $ -1 $ if there's no circle meeting the given conditions.

输入输出样例

输入样例 #1

7
6 2 4
2 3 1
2 4 10
5 3 4
1 3 2
2 5 4
4 3 2

输出样例 #1

8
-1
-1
-1
4
1
-1

说明

In the first test case, there's a desired circle of $ 8 $ people. The person with the number $ 6 $ will look at the person with the number $ 2 $ and the person with the number $ 8 $ will look at the person with the number $ 4 $ . In the second test case, there's no circle meeting the conditions. If the person with the number $ 2 $ is looking at the person with the number $ 3 $ , the circle consists of $ 2 $ people because these persons are neighbors. But, in this case, they must have the numbers $ 1 $ and $ 2 $ , but it doesn't meet the problem's conditions. In the third test case, the only circle with the persons with the numbers $ 2 $ and $ 4 $ looking at each other consists of $ 4 $ people. Therefore, the person with the number $ 10 $ doesn't occur in the circle.