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
Input will start an integer T (1≤T≤10) denoting the number of test cases.
In each test case, two space separated integers X (1≤X≤104) and P (1≤P≤1010) will be given.
Output
For each test case, print the minimum positive value of K in a single separate line.
If no such K exists, print -1.
Sample
Input
Output
2
123 9
123 10
3
-1
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.