P12567 [UOI 2023] An Array of Coins and Weighing Requests

**This is an interactive problem.** There are $n$ coins arranged in a row and numbered from $1$ to $n$ from left to right. Exactly $k$ ($k

See Interactive Protocol.

See Interactive Protocol.

Let's define $q$ as the maximum number of weighing queries you can make in the tests of a certain block. - ($5$ points): $n \le 16$, $q=16$; - ($9$ points): $k=1$, $q=16$; - ($7$ points): $k=1$, $q=11$; - ($16$ points): $k \le 16$, $q=11$; - ($9$ points): all fake coins have the same weight, $q=11$; - (up to $54$ points): $q=300$. Let the maximum number of weighings used be $c$. If $c \le 9$, you will get $54$ points, otherwise you will get $ \lfloor 54 \cdot \max(-0.0004 \cdot c + 0.3134, 0.018 + \frac{9.0773}{c}) \rfloor $ points. Here is the $\tt{C++}$ code that computes the number of points for the last block of tests depending on the number of weighings used: ```cpp ((c