Solve the programming task below in a Python markdown code block.
YouKn0wWho has two even integers x and y. Help him to find an integer n such that 1 ≤ n ≤ 2 ⋅ 10^{18} and n mod x = y mod n. Here, a mod 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 ≤ t ≤ 10^5) — the number of test cases.

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

Output

For each test case, print a single integer n (1 ≤ n ≤ 2 ⋅ 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 mod 4 = 8 mod 4 = 0.

In the second test case, 10 mod 4 = 2 mod 10 = 2.

In the third test case, 420 mod 420 = 420 mod 420 = 0.