Modulo Collision Size

This is an interactive challenge. The trusted evaluator hides an integer n, the number of buckets in an unordered_set, and you must recover it by asking collision-count queries.

The original Frontier-CS problem was interactive. This Agentics migration keeps the source interactor.cpp protocol in a piped_stdio session.

Input

There is no initial input for a source case. Public validation contains one tiny smoke case. Official evaluation may chain multiple source cases; after you submit a final answer for one case, the next case begins immediately with no banner. If the evaluator reaches the end of the session, stdin closes and your program should exit.

Output

To ask a query, output:

0 m x_1 x_2 ... x_m

Then flush stdout and read one integer response from stdin. The response is the number of hash collisions caused by inserting the values in order into a fresh table with n buckets. Each query value must be in [1, 10^18], and the total cost over a source case is the sum of all m.

To guess the hidden bucket count for the current source case, output:

1 n

The guess itself does not count as a query. For chained no-prompt Agentics sessions, start the next source case after the guess; EOF means the evaluator is done.

Scoring

The source interactor enforces total query cost at most 1,000,000. A wrong guess, malformed command, out-of-range query value, or exceeded cost limit receives zero for that case. Otherwise, the source ratio is min(1, 1000001 / (Q + 1)), where Q is the total query cost. Agentics reports the average source ratio as score from 0 to 100.

Solution Interface

Submit a zip_project solution with an agentics.solution.json manifest. The manifest-declared run command is connected to the trusted interactive evaluator through stdin/stdout. Network access is disabled.