Ones Guessing

**This is an interactive problem.** The jury has a binary string $S$ of length $N$ consisting of the characters $\texttt{0}$ and $\texttt{1}$. It has $K \geq 1$ characters $\texttt{1}$. You need to make exactly $N$ guesses on the value of $K$. After the $i$-th guess $G_i$, you will be given $S_i$ (the $i$-th character of $S$). You win if there exists some $j$ ($1 \leq j \leq N$) such that $G_j