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## Problem Description

There are *N* platforms in front of Jie Feng numbered 1 to *N*. Platform *i* is at height *i* metres from the ground.

Jie Feng wants to visit each platform **exactly** once. To do so, Jie Feng needs to make (*N* - 1) jumps between the platforms.

As it is dangerous for Jie Feng to make jumps where the difference in height is large, he has a jetpack to help him.

Before making any jump, in order to operate the jetpack, Jie Feng has to first input *K* **distinct** integers into the jetpack: the *jump heights* that the jetpack is allowed to operate on.

Jie Feng can only jump between two platforms if the absolute difference in their heights is one of the *K* integers Jie Feng has entered in the jetpack.

Moreover, to avoid damaging the jets in his jetpack, Jie Feng has to ensure that he utilizes every *jump height* at least once. This means that each of the *K* *jump heights* must be equal to the height difference between two platforms of at least one of the (*N* - 1) jumps Jie Feng makes.

Help Jie Feng to find any valid order to visit the platforms, and the *K* *jump heights* Jie Feng inputs for the order that you have found. It is guaranteed that there is at least one valid way to visit the platforms.

## Input

The only line of input contains two integers, *N*, the number of platforms, and *K*, the number of *jumps heights* Jie Feng needs to input.

## Output

On the first line, output *K* integers, the *jump heights* that Jie Feng needs to input into the jetpack.

On the following line, output *N* integers. The *i*th integer should indicate the *i*th platform that Jie Feng should visit.

## Limits

Subtask 1 (12%): 2 ≤ *N* ≤ 1 000 000. *K* = 1.

Subtask 1 (14%): 3 ≤ *N* ≤ 1 000 000. *K* = 2.

Subtask 3 (14%): 1 ≤ *K* < *N* ≤ 4.

Subtask 4 (19%): 1 ≤ *K* < *N* ≤ 11.

Subtask 5 (41%): 1 ≤ *K* < *N* ≤ 1 000 000.

Subtask 6 (0%): Sample Testcases

## Sample Testcase 1

### Input

6 2

### Output

2 5 2 4 6 1 3 5

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 12 | 6 | 0.5s | 256MB | Minimum |

2 | 14 | 14 | 0.5s | 256MB | Minimum |

3 | 14 | 6 | 0.5s | 256MB | Minimum |

4 | 19 | 50 | 0.5s | 256MB | Minimum |

5 | 41 | 70 | 0.5s | 256MB | Minimum |

6 | 0 | 1 | 0.5s | 256MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o platforms -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512