Description: 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 of two items with indices $$$i$$$ and $$$j$$$ ($$$i \neq j$$$) - What is the result of a bitwise 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 $$$3$$$. Input Format: It is guaranteed that for each element in a sequence the condition $$$0 \le a_i \le 10^9$$$ is satisfied. Output Format: None Note: 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)Notesand 2 52$$$a_2=6$$$, $$$a_5=3$$$. Interactor returns bitwise AND of the given numbers.or 5 67$$$a_5=3$$$, $$$a_6=5$$$. 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.