CF1556D Take a Guess

This is an interactive task William has a certain sequence of integers $ a_1, a_2, \dots, a_n $ in his mind, but due to security concerns, he does not want to reveal it to you completely. William is ready to respond to no more than $ 2 \cdot n $ of the following questions: - What is the result of a [bitwise AND](https://en.wikipedia.org/wiki/Bitwise_operation#AND) of two items with indices $ i $ and $ j $ ( $ i \neq j $ ) - What is the result of a [bitwise OR](https://en.wikipedia.org/wiki/Bitwise_operation#OR) of two items with indices $ i $ and $ j $ ( $ i \neq j $ ) You can ask William these questions and you need to find the $ k $ -th smallest number of the sequence. Formally the $ k $ -th smallest number is equal to the number at the $ k $ -th place in a 1-indexed array sorted in non-decreasing order. For example in array $ [5, 3, 3, 10, 1] $ $ 4 $ th smallest number is equal to $ 5 $ , and $ 2 $ nd and $ 3 $ rd are $ 3 $ .

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In the example, the hidden sequence is $ [1, 6, 4, 2, 3, 5, 4] $ . Below is the interaction in the example. Query (contestant's program) Response (interactor) Notes and 2 5 2 $ a_2=6 $ , $ a_5=3 $ . Interactor returns bitwise AND of the given numbers. or 5 6 7 $ a_5=3 $ , $ a_6=5 $ . Interactor returns bitwise OR of the given numbers. finish 5 $ 5 $ is the correct answer. Note that you must find the value and not the index of the kth smallest number.