Matrix K-th Smallest

The judge owns a hidden n x n matrix whose rows and columns are nondecreasing. Your task is to identify the k-th smallest matrix value.

At session start the evaluator writes:

n k

To inspect one cell, write QUERY x y, flush, and read the integer value at row x, column y. Coordinates are one-based and must be in [1, n].

To finish the current case, write DONE ans, flush, and continue reading. A positive n k starts another source case, while 0 0 means the Agentics session is complete and your program should exit. EOF before DONE, malformed commands, out-of-bounds queries, exceeding the source query limit, or a wrong final answer receive zero from the trusted evaluator. The trusted evaluator writes result.json; participant code must only speak the stdin/stdout protocol.

The official score is the original Frontier-CS query-efficiency score for a correct answer, scaled to score from 0 to 100.