Description

Given that $a, b$ are positive integers with $a \leq b$.

Find $x, y$ that satisfy the conditions and minimize $x + y$.

Conditions:

• $\gcd(x, y) = a$;
• $\mathrm{lcm}(x, y) = b$;
• $x \leq y$.

Input Format

Multiple test cases, terminated by EOF.

There are at most $10^3$ lines, each containing two numbers $a, b$.

Output Format

Output the same number of lines as in the input. For each line, output two numbers $x, y$, separated by a single space.

3 60

12 15

200 20000
300 30000
400 40000

800 5000
1200 7500
1600 10000

Hint

$3 \leq a, b < 2^{63}$.

Terminated by EOF; there is no line count $n$, and the first line is testdata.

The testdata are randomly generated.

Translated by ChatGPT 5