Codeforces Round 752 (Div. 1) |
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Finished |
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.
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).
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.
4 4 8 4 2 420 420 69420 42068
4 10 420 9969128
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, $$$420 \bmod 420 = 420 \bmod 420 = 0$$$.
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