There were $n$ coders from Aalto and $n$ coders from UH in a programming contest. It turned out that after the contest, each coder had a distinct score.

Your task is to find the $k$th highest score in the contest.

Interaction

This is a special task: you are not directly given the scores of the coders, but you can only ask a set of queries.

Your program should interact with the grader using standard input and output. Initially, the grader gives you the values of $n$ and $k$. After this, you may perform a set of queries. There are three types of queries:

• “1 $i$” where $1 \le i \le n$: get the $i$th highest score for Aalto
• “2 $i$” where $1 \le i \le n$: get the $i$th highest score for UH
• “3 $s$”: report that the $k$th highest score is $s$

You are allowed to perform at most $100$ queries, and your program must terminate after performing a query of type $3$.

Constraints

• $1 \le n \le 10^5$
• $1 \le k \le 2n$
• each score is between $1$ and $10^9$

Note

In some languages, you may need to flush the output after printing a line. Do not use efficient I/O methods.

Example

Assume that $n=3$, $k=1$ and the scores for Aalto are $[9,4,3]$ and the scores for UH are $[8,6,1]$. Here is an example of a valid interaction:

• Grader outputs:

3 1

• Your program outputs:

1 1

• Grader outputs:

9

• Your program outputs:

2 1

• Grader outputs:

8

• Your program outputs:

3 9