**Time limit:**1.00 s**Memory limit:**512 MB

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 $s$

**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`