2008H - Тест Сакурако

Editorial says Let's fix one x and try to solve this task for it.

okay makes our time complexity q*(something), moving on...

How to find number of i that ai mod x ≤ m for some m

We can use binary search of some sort, making our complexity

q*log(x)*checkerForM, how in the world is this complexity not TLE

Can anyone explain it to me.