K-Foldable String

You are given a binary string $S$ with length $N$ and an integer $K$, which is a divisor of $N$. A string is said to be $K$*-foldable* if it can be changed to a string with length $K$ by repeating the following process without any *collisions* (defined below): - Select the prefix of the current string $S$ with length $2K$. (Note that as long as the length of $S$ is greater than $K$, this prefix a