[Solution] Maximize Difference CodeChef Solution 2022

Problem

Chef has two numbers $N$ and $M$. He calls a pair of numbers $(A, B)$ good if it satisfies the following conditions:

• $1 \le A, B \le M$
• $\gcd(A, B) \ge N$

Chef wants to find a good pair $(A, B)$ such that the value of $|A - B|$ is maximized. Can you help Chef? (Here $|X|$ represents the absolute value of $X$).

If there are multiple good pairs for which the value of $|A - B|$ is maximized, you can print any of them. It can be proved that under the given constraints, at least one good pair always exists.

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Input Format

• The first line contains a single integer $T$ — the number of test cases. Then the test cases follow.

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• The first line of each test case contains two integers $N$ and $M$ — the parameters mentioned in the statment.

Output Format

For each test case, output two integers $A$ and $B$ such that $(A, B)$ is a good pair and the value of $|A - B|$ is maximized.

Explanation:

Test case $1$: $(5, 5)$ and $(6, 6)$ are the only good pairs and for both of them the value of $|A - B|$ is $0$.

Test case $2$: $(6, 8), (8, 6), (2, 8), (8, 2), (4, 6), (6, 4), (2, 6), (6, 2), (2, 4), (4, 2)$ and $(2, 2)$ are the good pairs out of which $|A - B|$ is maximum for $(2, 8)$ and $(8, 2)$.