\problemname{Sequence Guessing}

You are tasked with creating a secret sequence of integers that is difficult to guess.

The sequence is subject to the following constraints:
\begin{itemize}
  \item The first number in the sequence must be $0$.
  \item The last number in the sequence must be $100\,000$.
  \item Each number in the sequence must be either $1$ or $2$ greater than the one preceding it.
\end{itemize}

At first, all you need to reveal is the length of the sequence.

Then, an adversary will guess the numbers in the sequence one at a time.
\begin{itemize}
  \item If the guessed number is in your sequence, you must reveal exactly where in the sequence it appears.
  \item If the guessed number is not in your sequence, you must simply reveal that it is not in the sequence.  This is considered a ``miss''.
\end{itemize}
Note that because you are not forced to write down the sequence in advance, you can ``cheat''
by changing the sequence you have in mind, so long as it does not contradict the information you
have revealed so far. It turns out that under these conditions, you can always force the
adversary to get $33\,333$ misses before they can guess every number in your sequence. Your job
is to write a program that does so.

\section*{Interaction}

This is an interactive problem.

Your program should begin by printing $k$ $(2 \leq k \leq 100\,001)$, the length of your sequence, as a single integer on a single line.
After this, you will receive one integer $x$ on a single line.
This integer is guaranteed to be between $-1$ and $100\,000$ inclusive.

\begin{itemize}
  \item If $x = -1$, the adversary has given up;
  your program should print all $k$ integers in your sequence in order,
  one line per integer, and then exit.
  The adversary is guaranteed to give this input after it has gotten $33\,333$ misses,
  though it may do so earlier. After printing all $k$ integers,
  your program should exit.
  If you print a valid sequence consistent with your previous responses,
  your submission will be considered correct for this test case. 
  \item If $x$ is not in your sequence, print $-1$ on a single line.
  \item If $x$ is in your sequence, print a single integer $i$ on a single line,
  such that $x$ is the $i$th (1-indexed) number in the sequence.
  If you have printed every integer from $1$ to $k$,
  your program should now exit, and your submission will receive a Wrong Answer verdict.
\end{itemize}

Do not forget to flush the output after every integer you print.

After this, if your program has not yet exited, the process will repeat, with you receiving another single integer.
The adversary is guaranteed to never repeat integers.

The adversary may employ different guessing strategies on different runs.