By Dilson Guimarães, UFMG Brazil
Alexandre, Dilson, Filipe and Lucas need prepare questions for the Seletiva UFMG 2014 and thought in the following problem.
Luiz is the newest intern of a company that develop electronic equipment. One of his first tasks is to connect pins of two components, using connections in a straight line. Each one of the two components has N pins, numbered from 1 to N. The pins of the same number should be connected by a straight line. The figure below shows an example.
The pins of left component are always numbered from up to down. Unfortunately, the same does not happen with the pins in the right component and is necessary crossed connections. Luiz need compute the maximum amount of connections that need be done, in a way that two connections never cross, what is 3 in the example. Luiz doesn't know how to programming and ask you for your help in this task. The input is composed by the number of pins, N, and the numeration sequence of the second component.
The illustrious creators of this problem are very worried recently and they don't have time to generate test cases. Because of that, your task is to write test cases with N pins that the answer be K. Therefore, in the next contest, your test cases generator could be used as the proposed problem.
The input is composed by two integers, N and K (1 ≤ K ≤ N ≤ 106), indicating the number of pins and the answer desired. The input ends with N=K=0.
For each test case, output one line with one sequence of N integers separated by spaces. This sequence should represent the numeration of the pins in the right component such that the answer of the proposed problem be K. If exist many solutions, write the smallest lexicographically.
|Input Sample||Output Sample|
1 5 4 3 2