X. Nice Guess

Task

$A$ and $B$ are playing a mind-bending game. $A$ has an unknown number, $x$, which $B$ needs to guess. The function guess(v) returns $1$ if $v \geq x$, $0$ otherwise. Use the minimum number of calls to the guess function to score $100$ points.

Interaction Protocol

The contestant must implement the function with the header:
int solve(void);

The contestant can use the function defined in interaction.h with the header:
int guess(int val);

Constraints and clarifications

• $1 \leq x \leq 1\ 000\ 000\ 000$
• Let $k$ be the number of calls to the guess function made by the contestant.
• For tests worth $10$ points, $k$ can be at most $32$.
• For the other tests, $k$ should be at most $0$.
• You can use the sample grader from the attachments.
• This video could prove helpful in finding the $100$ point solution.

Example interaction

Let $x = 5$.

The grader calls the function solve().

The contestant guesses $6$, where guess(6) = $1$.

The contestant guesses $4$, where guess(4) = $0$.

The function solve() returns $5$.

The number of calls to the guess function is $2$, which is sufficient for the $10$-point subtask but not sufficient for the rest.