Guess Two Strings

This is an interactive problem.

Jury has chosen two secret binary strings of length $N$ and called them $s$ and $t$ such that $s$ is not lexicographically greater than $t$. Your task is to find out which strings were chosen. To do that, you can ask the jury to generate up to $Q$ strings. Each such string $r$ will be generated in the following way:

1. start by assigning $r = s$ or $r = t$, choosing one of them randomly with equal probability,
2. randomly select $K$ distinct positions in the string $r$ so that each set of $K$ positions has equal probability of being selected,
3. flip the digits at the selected positions in $r$: change all "0"s to "1"s and all "1"s to "0"s,
4. give the modified string $r$ to you.

Note that $s$ and $t$ don't change during generation of string $r$.

Your task is to correctly guess $s$ and $t$.

This example violates the constraints, and is given only to illustrate the process of interaction. All tests in the testing system will satisfy all the constraints from the statement.