L. Coordinate Paper
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Once there was a contest, where the last problem was about coordinate paper. You were given a piece of coordinate paper, where there were grids of $$$n$$$ rows and $$$10^{100}$$$ columns. The grids were initially white, and you might paint some of them black. In that problem, you were required to paint the paper in a special way. Suppose the number of black grids in the $$$i$$$-th row is $$$a_i$$$. Your painting was supposed to satisfy that

  1. for any $$$i$$$, $$$a_i \geq 0$$$.
  2. $$$\sum_{i=1}^n a_i = s$$$.
  3. for any $$$i \in \{1, \dots, n - 1\}$$$, either $$$a_i - a_{i+1} = k$$$ or $$$a_{i+1} - a_i = 1$$$.

Can you still find an answer to that problem?

Input

The only line contains three integers $$$n$$$, $$$k$$$ and $$$s$$$ ($$$1 \leq n, k \leq 10^5$$$, $$$1 \leq s \leq 10^{18}$$$).

Output

If there is no solution, print "-1" (without quotes).

Otherwise, print the $$$n$$$ integers $$$a_1, \ldots, a_n$$$. Any answer satisfying all requirements will be accepted.

In this problem, extra blank characters will be ignored when your answer is judged.

Example
Input
3 2 15
Output
6 4 5