RoAlgo PreOJI 2024 VI | operatii

Task

You are given three natural numbers, $a$, $b$, and $k$. George, being passionate about mathematics and computer science, has invented an algorithm, and now he wants to test your computer science knowledge to find the answers he is looking for.

The algorithm described by George works as follows:

As long as $a$ and $b$ are different, print $a$ and $b$ on a new line and subtract the smaller number from the larger one.

For example, if initially $a = 14$ and $b = 39$, the first $5$ pairs of displayed values are:

• $14 \ 39$ (first pair)
• $14 \ 25$ (subtract $a$ from $b$)
• $14 \ 11$ (subtract $a$ from $b$)
• $3 \ 11$ (subtract $b$ from $a$)
• $3 \ 8$ (subtract $a$ from $b$)

Now, George wants to know what the values of $a$ and $b$ will be at the $k$-th step.

Practically, if $k$ is $3$, you should print $14 \ 11$.

Since this is too easy, he asks you to solve the problem for $t$ such triplets. He guarantees that the algorithm will display at least $k$ lines.

Input data

The first line of the input file operatii.in will contain $t$, the number of triplets for which you need to solve the problem.

The following $t$ lines contain the triplets, each containing $a \ b \ k$, the three numbers of the triplet.

Output data

For each triplet, print on a separate line in the file operatii.out the value of $a$ and the value of $b$ after $k$ steps.

Constraints and clarifications

• $1 \leq t \leq 1\ 000$;
• $1 \leq a, b, k \leq 10^9$;
• The algorithm will display at least $k$ lines.
• For tests worth $15$ points, $(t = 1)$ and $(1 \leq a, b, k \leq 10^6)$.
• For tests worth $25$ points, $(1 \leq t \leq 5)$ and $(1 \leq a, b, k \leq 10^6)$.

Example

operatii.in

2
14 39 3
167 96 7

operatii.out

14 11
17 4

Explanation

For the first pair, the explanation is found in the statement.

For the second pair, the values of $a$ and $b$ change as follows:

• $167 \ 96$
• $71 \ 96$
• $71 \ 25$
• $46 \ 25$
• $21 \ 25$
• $21 \ 4$
• $17 \ 4$

We will print $17 \ 4$.