Timovi

Time limit1sMemory limit64 MB

Summary

Kids are dealt into N teams in a bouncing 1..N..1 order, K per visit, until fewer than K remain; report each team's final count.

Level: Medium4 of 10
Topics: Math, Simulation, Implementation, Array
Solved: No attempts yet

Problem

You split $M$ kids into $N$ teams. First you put $K$ kids into the first team, then $K$ kids into the second team, and so on up to the $N$ th team. After the $N$ th team you turn around and keep putting $K$ kids into each team, going from the $(N-1)$ th team down to the first team. After the first team you turn around again, continue from the second team up to the $N$ th team, and repeat until no kids are left to hand out.

For example, with three teams the kids go into the teams in this order: 1, 2, 3, 2, 1, 2, 3, and so on.

If fewer than $K$ kids are left when a team comes up, that team takes every remaining kid and the process ends.

Report how many kids each team holds once the process ends.

Input

The first line contains the integers $N$ , $K$ and $M$ ( $2 \le N \le 200\,000$ , $1 \le K \le M \le 2\,000\,000\,000$ ).

Output

Print the number of kids in each of the $N$ teams on a single line, from the first team to the $N$ th team, separated by single spaces.

Examples3

Example 1
Input
```
2 1 3
```
Expected output
```
2 1
```
Example 2
Input
```
3 2 7
```
Expected output
```
2 3 2
```
Example 3
Input
```
4 5 6
```
Expected output
```
5 1 0 0
```