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 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 $3$ .

It is guaranteed that for each element in a sequence the condition $0 \le a_i \le 10^9$ is satisfied.

In the first line you will be given two integers $n$ and $k$ $(3 \le n \le 10^4, 1 \le k \le n)$ , which are the number of items in the sequence $a$ and the number $k$ .

After that, you can ask no more than $2 \cdot n$ questions (not including the "finish" operation).

Each line of your output may be of one of the following types:

• "or i j" $(1 \le i, j \le n, i \neq j)$ , where $i$ and $j$ are indices of items for which you want to calculate the bitwise OR.
• "and i j" $(1 \le i, j \le n, i \neq j)$ , where $i$ and $j$ are indices of items for which you want to calculate the bitwise AND.
• "finish res", where $res$ is the $k$ th smallest number in the sequence. After outputting this line the program execution must conclude.

In response to the first two types of queries, you will get an integer $x$ , the result of the operation for the numbers you have selected.

After outputting a line do not forget to output a new line character and flush the output buffer. Otherwise you will get the "Idleness limit exceeded". To flush the buffer use:

• fflush(stdout) in C++
• System.out.flush() in Java
• stdout.flush() in Python
• flush(output) in Pascal
• for other languages refer to documentation

If you perform an incorrect query the response will be $-1$ . After receiving response $-1$ you must immediately halt your program in order to receive an "Incorrect answer" verdict.

Hacking

To perform a hack you will need to use the following format:

The first line must contain two integers $n$ and $k$ $(3 \le n \le 10^4, 1 \le k \le n)$ , which are the number of items in the sequence $a$ and the number $k$ .

The second line must contain $n$ integers $a_1, a_2, \dots, a_n$ $(0 \le a_i \le 10^9)$ , the sequence $a$ .

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.