One day, the schoolboy Mark misbehaved, so the teacher Sasha called him to the whiteboard.

Sasha gave Mark a table with $n$ rows and $m$ columns. His task is to arrange the numbers $0, 1, \ldots, n \cdot m - 1$ in the table (each number must be used exactly once) in such a way as to maximize the sum of MEX$^{\text{∗}}$ across all rows and columns. More formally, he needs to maximize $$\sum\limits_{i = 1}^{n} \operatorname{mex}(\{a_{i,1}, a_{i,2}, \ldots, a_{i,m}\}) + \sum\limits_{j = 1}^{m} \operatorname{mex}(\{a_{1,j}, a_{2,j}, \ldots, a_{n,j}\}),$$ where $a_{i,j}$ is the number in the $i$-th row and $j$-th column.

Sasha is not interested in how Mark arranges the numbers, so he only asks him to state one number — the maximum sum of MEX across all rows and columns that can be achieved.

Input

Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 10^9$) — the number of rows and columns in the table, respectively.

Output

For each test case, output the maximum possible sum of $\operatorname{mex}$ across all rows and columns.

见题面 Input 部分

见题面 Output 部分

In the first test case, the only element is $0$, and the sum of the $\operatorname{mex}$ of the numbers in the first row and the $\operatorname{mex}$ of the numbers in the first column is $\operatorname{mex}(\{0\}) + \operatorname{mex}(\{0\}) = 1 + 1 = 2$.

In the second test case, the optimal table may look as follows:

$3$$0$$2$$1$

Then $\sum\limits_{i = 1}^{n} \operatorname{mex}(\{a_{i,1}, a_{i,2}, \ldots, a_{i,m}\}) + \sum\limits_{j = 1}^{m} \operatorname{mex}(\{a_{1,j}, a_{2,j}, \ldots, a_{n,j}\}) = \operatorname{mex}(\{3, 0\}) + \operatorname{mex}(\{2, 1\})$ $+ \operatorname{mex}(\{3, 2\}) + \operatorname{mex}(\{0, 1\}) = 1 + 0 + 0 + 2 = 3$.