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I am Good

By Zeronfinity · Limits 2s, 512 MB

I am trying to become a good guy, because it doesn’t take money to become good. So here’s a short and simple problem statement because I am a good guy! :)

Given two integers $X$ and $P$, find the minimum positive value of $K$ such that $f(X, K)$ is divisible by $P$.

$f(X, K)$ is defined as the $K$-times concatenation of the integer $X$ (without leading zeroes).

For example, $f(123, 3) = 123123123$,
$f(54, 4) = 54545454$,
$f(123, 2) = 123123$,
$f(7, 5) = 77777$


Input will start an integer $T$ denoting the number of test cases.

In each test case, two space separated integers $X$ and $P$ will be given.


$1 \leq T \leq 10$
$1 \leq X \leq 10^4$
$1 \leq P \leq 10^{10}$


For each test case, print the minimum positive value of $K$ in a single separate line.
If no such $K$ exists, print -1.


123 9
123 10

In the first test case, $f(123,3)=123123123$ is divisible by 9 while $123123$ and $123$ are not divisible by 9. Thus 3 is the minimum possible value of $K$ for this test case.

In the second test case, $f(123,K)$ can never be divisible by 10 no matter what $K$ is.



17% Solution Ratio

EgorKulikovEarliest, 3w ago

EgorKulikovFastest, 0.0s

EgorKulikovLightest, 131 kB

rebornShortest, 1076B


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