Number Transformation Codeforces Solution | Codeforces Problem Solution 2022

Number Transformation Codeforces Solution | Codeforces Problem Solution 2022

A. Number Transformation

time limit per test

2 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

You are given two integers 𝑥$x$ and 𝑦$y$. You want to choose two strictly positive (greater than zero) integers 𝑎$a$ and 𝑏$b$, and then apply the following operation to 𝑥$x$ exactly 𝑎$a$ times: replace 𝑥$x$ with 𝑏⋅𝑥$b\cdot x$.

You want to find two positive integers 𝑎$a$ and 𝑏$b$ such that 𝑥$x$ becomes equal to 𝑦$y$ after this process. If there are multiple possible pairs, you can choose any of them. If there is no such pair, report it.

For example:

• if 𝑥=3$x=3$ and 𝑦=75$y=75$, you may choose 𝑎=2$a=2$ and 𝑏=5$b=5$, so that 𝑥$x$ becomes equal to 3⋅5⋅5=75$3\cdot 5\cdot 5=75$;
• if 𝑥=100$x=100$ and 𝑦=100$y=100$, you may choose 𝑎=3$a=3$ and 𝑏=1$b=1$, so that 𝑥$x$ becomes equal to 100⋅1⋅1⋅1=100$100\cdot 1\cdot 1\cdot 1=100$;
• if 𝑥=42$x=42$ and 𝑦=13$y=13$, there is no answer since you cannot decrease 𝑥$x$ with the given operations.

Solution Click Below:-  CLICK HERE

Input

The first line contains one integer 𝑡$t$ (1≤𝑡≤104$1\le t\le {10}^4$) — the number of test cases.

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Each test case consists of one line containing two integers 𝑥$x$ and 𝑦$y$ (1≤𝑥,𝑦≤100$1\le x,y\le 100$).

Output

If it is possible to choose a pair of positive integers 𝑎$a$ and 𝑏$b$ so that 𝑥$x$ becomes 𝑦$y$ after the aforementioned process, print these two integers. The integers you print should be not less than 1$1$ and not greater than 109${10}^9$ (it can be shown that if the answer exists, there is a pair of integers 𝑎$a$ and 𝑏$b$ meeting these constraints). If there are multiple such pairs, print any of them.

If it is impossible to choose a pair of integers 𝑎$a$ and 𝑏$b$ so that 𝑥$x$ becomes 𝑦$y$, print the integer 0$0$ twice.

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