Hidden Sequence

You did it! You have finally made it to the X spot of the treasure map, but to open the treasure chest, you first need to break the code. The label attached to the chest states the rules: the code is a binary sequence of length $N$, and to find this sequence you are allowed to ask questions of the following type: "is $S$ a subsequence of the hidden sequence?"

A binary sequence $S$, with values $S_1, S_2, \ldots, S_K$, is a subsequence of the code $C$, with values $C_1, C_2, \ldots, C_N$, if and only if $S$ can be obtained by deleting some of the values of $C$. Formally, $S$ is a subsequence of $C$ if and only if there exist $K$ indices $1 \le i_1 < i_2 < \cdots < i_K \le N$ such that $C_{i_j} = S_j$ for every $1 \le j \le K$.

You get a part of the treasure if you crack the code. The shorter the longest query you asked, the more of the treasure you get. In this game, the treasure is worth 100 points.