Binary String Xor

Chef has a binary string $S$ of length $N$. He wonders if it is possible to divide $S$ into exactly $K$ non-empty [substrings](https://en.wikipedia.org/wiki/Substring) such that each $S_i$ belongs to exactly one substring and the $\texttt{XOR}$ of each substring is the same. Can you help Chef to determine if it is possible to do so? Note: $\texttt{XOR}$ of substring $S_{L \cdots R}$ is defined as