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

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 kth 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 ith highest score for Aalto
- “2 i” where 1 \le i \le n: get the ith highest score for UH
- “3 s”: report that the kth 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