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 $$$a$$$.
7 6 2 7
and 2 5 or 5 6 finish 5
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. |
