A Variety of Operations

题意翻译

有两个数 $a,b$ 在一开始均为 $0$。现在每一步任选正整数 $k$ 进行如下三种操作之一： + 将 $a,b$ 同时加上 $k$ + 将 $a$ 加上 $k$，同时将 $b$ 减去 $k$ + 将 $b$ 加上 $k$，同时将 $a$ 减去 $k$ 现在给出 $t$ 组询问，每组询问给出 $c,d$，求出使 $a=c$ 且 $b=d$ 需要的最小操作次数，若不可能则输出 `-1`。

题目描述

William has two numbers $ a $ and $ b $ initially both equal to zero. William mastered performing three different operations with them quickly. Before performing each operation some positive integer $ k $ is picked, which is then used to perform one of the following operations: (note, that for each operation you can choose a new positive integer $ k $ ) 1. add number $ k $ to both $ a $ and $ b $ , or 2. add number $ k $ to $ a $ and subtract $ k $ from $ b $ , or 3. add number $ k $ to $ b $ and subtract $ k $ from $ a $ . Note that after performing operations, numbers $ a $ and $ b $ may become negative as well. William wants to find out the minimal number of operations he would have to perform to make $ a $ equal to his favorite number $ c $ and $ b $ equal to his second favorite number $ d $ .

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). Description of the test cases follows. The only line of each test case contains two integers $ c $ and $ d $ $ (0 \le c, d \le 10^9) $ , which are William's favorite numbers and which he wants $ a $ and $ b $ to be transformed into.

输出格式

For each test case output a single number, which is the minimal number of operations which William would have to perform to make $ a $ equal to $ c $ and $ b $ equal to $ d $ , or $ -1 $ if it is impossible to achieve this using the described operations.

输入输出样例

输入样例 #1

6
1 2
3 5
5 3
6 6
8 0
0 0

输出样例 #1

-1
2
2
1
2
0

说明

Let us demonstrate one of the suboptimal ways of getting a pair $ (3, 5) $ : - Using an operation of the first type with $ k=1 $ , the current pair would be equal to $ (1, 1) $ . - Using an operation of the third type with $ k=8 $ , the current pair would be equal to $ (-7, 9) $ . - Using an operation of the second type with $ k=7 $ , the current pair would be equal to $ (0, 2) $ . - Using an operation of the first type with $ k=3 $ , the current pair would be equal to $ (3, 5) $ .