Greedy Tree Blackbox

This is an interactive challenge. The evaluator first prints:

n ty

The hidden object is a rooted tree on vertices 1..n. Every internal node has at least two children. ty is a source test identifier and has no algorithmic effect.

For a query, print one line:

? sz v1 v2 ... vsz

The vi values must be distinct vertices in [1, n]. The evaluator scans the sequence from left to right, greedily keeps a node only when it is neither an ancestor nor a descendant of any already kept node, and replies with the number of kept nodes. Flush after every query.

To answer, print one line:

! p1 p2 ... pn

pi is the parent of vertex i; the root must have parent 0. Flush and then continue reading for another source case or exit on EOF.

The trusted evaluator owns the hidden parent array, rejects duplicate or out-of-range query elements, validates the exact parent array, and writes result.json. Source scoring gives full credit through 45000 queries, zero at or above 200000, and the original clamped linear ratio between those counts.