This problem is interactive.
You should guess hidden number $$$x$$$ which is between $$$1$$$ and $$$M = 10004205361450474$$$, inclusive.
You could use up to $$$5$$$ queries.
In each query, you can output an increasing sequence of $$$k \leq x$$$ integers, each between $$$1$$$ and $$$M$$$, inclusive, and you will obtain one of the following as an answer:
See the interaction section for clarity.
Be aware that the interactor is adaptive, i.e. the hidden number can depend on queries the solution makes. However, it is guaranteed that for any solution the interactor works non-distinguishable from the situation when the hidden number is fixed beforehand.
Hacks are allowed only with fixed hidden number. A hack is represented by a single integer between $$$1$$$ and $$$M$$$. In all pretests the hidden number is fixed as well.
You can make up to $$$5$$$ queries. To make a query print a number $$$k$$$ ($$$1 \le k \le 10^4$$$) and then an increasing sequence $$$t_0 < t_1 < \ldots < t_{k-1}$$$ of $$$k$$$ numbers, each between $$$1$$$ and $$$M$$$, inclusive. If $$$k > x$$$, you lose.
You get one integer as a response.
After printing a query do not forget to output end of line and flush the output. Otherwise you will get Idleness limit exceeded. To do this, use:
2
0
-1
2 2 3
2 20 30
3 5 7 9
In the first example the number $$$5$$$ is hidden.
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