HZNUOJ

NEW RDSP MODE I

Tags:
Time Limit:  1 s      Memory Limit:   32 MB
Submission:41     AC:26     Score:98.59

Description

Little A has became fascinated with the game Dota recently, but he is not a good player. In all the modes, the rdsp Mode is popular on online, in this mode, little A always loses games if he gets strange heroes, because, the heroes are distributed randomly.

Little A wants to win the game, so he cracks the code of the rdsp mode with his talent on programming. The following description is about the rdsp mode:

There are N heroes in the game, and they all have a unique number between 1 and N. At the beginning of game, all heroes will be sorted by the number in ascending order. So, all heroes form a sequence One.

These heroes will be operated by the following stages M times:

  1. Get out the heroes in odd position of sequence One to form a new sequence Two;
  2. Let the remaining heroes in even position to form a new sequence Three;
  3. Add the sequence Two to the back of sequence Three to form a new sequence One.

After M times' operation, the X heroes in the front of new sequence One will be chosen to be Little A's heroes. The problem for you is to tell little A the numbers of his heroes.

Input

There are several test cases.

Each case contains three integers N (1<=N<1,000,000), M (1<=M<100,000,000), (1<=X<=20).

Proceed to the end of file.

Output

For each test case, output X integers indicate the number of heroes. There is a space between two numbers. The output of one test case occupied exactly one line.

Samples

input
5 1 2 5 2 2
output
2 4 4 3

Hint

In case two: N=5,M=2,X=2, the initial sequence One is 1,2,3,4,5. After the first operation, the sequence One is 2,4,1,3,5. After the second operation, the sequence One is 4,3,2,1,5. So,output 4 3.

Source

辽宁省赛2010