Migrated from Lutece 1040 Great Inversion

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Description

There is an array $A$ with length of $n$. $A_i (1 \leq A_i \leq m)$ is the $i_{th}$ element in $A$. Please find a possible situation of $A$ so that the inversion number is exactly $K$.

Input

Only three integers indicating $n$, $m$, $k$.

$1 \leq m \leq n \leq 1000, 1 \leq k \leq 1000000$

Output

$n$ numbers in a line indicating $A$ if there is a solution, If there are multiple solutions, you may print any of them. Otherwise output -1 instead.

Samples

5 3 2

1 1 2 1 1

Note

Inversion

Resources

The 13th UESTC Programming Contest Preliminary