B. Moderate Modular Mode
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

YouKn0wWho has two even integers $$$x$$$ and $$$y$$$. Help him to find an integer $$$n$$$ such that $$$1 \le n \le 2 \cdot 10^{18}$$$ and $$$n \bmod x = y \bmod n$$$. Here, $$$a \bmod b$$$ denotes the remainder of $$$a$$$ after division by $$$b$$$. If there are multiple such integers, output any. It can be shown that such an integer always exists under the given constraints.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$)  — the number of test cases.

The first and only line of each test case contains two integers $$$x$$$ and $$$y$$$ ($$$2 \le x, y \le 10^9$$$, both are even).

Output

For each test case, print a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^{18}$$$) that satisfies the condition mentioned in the statement. If there are multiple such integers, output any. It can be shown that such an integer always exists under the given constraints.

Example
Input
4
4 8
4 2
420 420
69420 42068
Output
4
10
420
9969128
Note

In the first test case, $$$4 \bmod 4 = 8 \bmod 4 = 0$$$.

In the second test case, $$$10 \bmod 4 = 2 \bmod 10 = 2$$$.

In the third test case, $$$420 \bmod 420 = 420 \bmod 420 = 0$$$.