A. A Variety of Operations
math
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 \(k\)) add number \(k\) to both \(a\) and \(b\), or add number \(k\) to \(a\) and subtract \(k\) from \(b\), or 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 \(d\).
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.
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.
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 \((3, 5)\).