Help Vasilisa the Wise 2 · Interview Problem

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Codeforces

Easy

Math

Number Theory

Simulation

Help Vasilisa the Wise 2

Find a pair of integers that satisfies simple arithmetic conditions around a given sum and difference.

Acceptance 0%

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Problem Statement

Problem

You are given three integers $x$ , $y$ , and $k$ .

Find any pair of integers $(a, b)$ such that:

$a + b = x$ ,
$|a - b| = y$ ,
and both $a$ and $b$ are divisible by $k$ .

If such a pair exists, print it in any order. Otherwise, report that it is impossible.

This is a small constructive arithmetic task: you only need to determine whether the conditions can be satisfied and, if so, output one valid pair.

Input Format

The input contains three integers $x$ , $y$ , and $k$ .

Output Format

If a valid pair exists, output two integers $a$ and $b$ separated by a space. Otherwise, output -1.

Constraints

The values are integers.
You only need to produce one valid pair if it exists.
If no pair satisfies all conditions, output -1.

Examples

Sample cases returned by the problem API.

Example 1

Input

10 2 2

Output

6 4

Explanation

The pair $6 $and \$ 4 $sums to \$ 10 $, their difference is \$ 2 $, and both are divisible by \$ 2$.

Example 2

Input

10 3 2

Output

-1

Explanation

No integers can have sum $10 $and absolute difference \$ 3 $while both being divisible by \$ 2$.

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