A. Restoring Numbers

Codeforces

IDCF10175A

Time2000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Pavel had two positive integers a and b. He found their sum s and greatest common divisor g, and forgot a and b after that. Help him to restore the original numbers. A single line contains two integers s and g (1 ≤ s ≤ 109, 1 ≤ g ≤ 109) — sum and greatest common divisor of the numbers a and b. If Pavel made a mistake and there are no such numbers a and b, output a single number - 1. Otherwise, output two positive integers a and b on a single line, separated by a space. If there are multiple possible solutions, output any of them. ## Input A single line contains two integers s and g (1 ≤ s ≤ 109, 1 ≤ g ≤ 109) — sum and greatest common divisor of the numbers a and b. ## Output If Pavel made a mistake and there are no such numbers a and b, output a single number - 1.Otherwise, output two positive integers a and b on a single line, separated by a space. If there are multiple possible solutions, output any of them. [samples]

**Definitions** Let $ s, g \in \mathbb{Z}^+ $ be given, with $ 1 \leq s, g \leq 10^9 $. **Constraints** Find positive integers $ a, b \in \mathbb{Z}^+ $ such that: 1. $ a + b = s $ 2. $ \gcd(a, b) = g $ **Objective** If such $ a, b $ exist, output any pair $ (a, b) $. Otherwise, output $ -1 $.

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