Mod Equality

You are given $N$ non-negative integers $A_1, A_2, \ldots, A_N$. You are allowed to perform following operation any number of times: - Choose any valid index $i$ ($1 \le i \le N$) and a positive integer $M>0$ and replace $A_i$ with $A_i\bmod M$. That is, replace $A_i$ with its remainder when divided by $M$, which is a value between $0$ and $M-1$, inclusive. - $M$ does not need to be same between