Time Limit: 1 s
Memory Limit: 32 MB

Submission：41
AC：26
Score：98.59

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:

- Get out the heroes in odd position of sequence One to form a new sequence Two;
- Let the remaining heroes in even position to form a new sequence Three;
- 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.

There are several test cases.

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

Proceed to the end of file.

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.

input

5 1 2
5 2 2

output

2 4
4 3

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.