We need to arrange ~M~ kids in ~N~ teams. We begin by placing ~K~ kids in each team, starting from the first to the ~N^\text{th}~ team. When we finish with the ~N^\text{th}~ team, we switch directions and continue, placing ~K~ kids in each team, from the ~(N - 1)^\text{th}~ to the first team, respectively. When we finish with the first team, we switch directions again and continue the process from the second to the ~N^\text{th}~ team, respectively, and so on until there are no kids left to distribute. For example, if we have three teams, we will place ~K~ kids in teams in the following order: first team, second team, third team, second team, first team, second team, etc.

If at any point, there are less than ~K~ kids left to place in the current team, we place all the remaining kids in that team and end the process.

Output the number of kids in each team when the process ends.

Input Specification

The first line of input contains the integers ~N~ ~(2 \le N \le 200\,000)~, ~K~ and ~M~ ~(1 \le K \le M \le 2\,000\,000\,000)~ from the task.

Output Specification

In a single line, output the number of kids in each of the ~N~ teams, respectively from the first to the ~N^\text{th}~ team.

Scoring

In test cases worth a total of ~40~ points, it will hold ~M / K \le 200\,000~.

Sample Input 1

2 1 3

Sample Output 1

2 1

Sample Input 2

3 2 7

Sample Output 2

2 3 2

Sample Input 3

4 5 6

Sample Output 3

5 1 0 0