Danya and Numbers

Danya has a sequence $A$ of non-negative integers. Initially, $A$ has length $N$. Let's define a function $f(x, A)$, where $x$ is a positive integer $\le |A|$, as the maximum of bitwise ANDs of all subsequences of $A$ with length equal to $x$. Kostya gives Danya $M$ requests. There are three types of requests: - $1\;v$: append an integer $v$ to $A$ - $2\;v$: delete an element equal to $v$ from $