K - balanced string

A binary string $S$ of length $N$ is called *$K$-balanced string* if it holds the following property: For each index $i\;(1 \leq i \leq N)$ such that $S_i = $ '1', there must exist an index $j\;(1 \leq j \leq N)$ such that $S_j = $ '1' and $\mid i - j \mid = K$, where $\mid x \mid$ denotes the absolute value of $x$. For example, if $K = 1$, "00", "110", "011011" are 1-balanced strings, while "01