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.

$$$^{\text{∗}}$$$The minimum excluded (MEX) of a collection of integers $$$c_1, c_2, \ldots, c_k$$$ is defined as the smallest non-negative integer $$$x$$$ which does not occur in the collection $$$c$$$.

For example:

$$$\operatorname{mex}([2,2,1])= 0$$$, since $$$0$$$ does not belong to the array.
$$$\operatorname{mex}([3,1,0,1]) = 2$$$, since $$$0$$$ and $$$1$$$ belong to the array, but $$$2$$$ does not.
$$$\operatorname{mex}([0,3,1,2]) = 4$$$, since $$$0$$$, $$$1$$$, $$$2$$$, and $$$3$$$ belong to the array, but $$$4$$$ does not.

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.

Note

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

MEX Table

Examples