Construct an array of size $n$ with $a \leq n$ 0s and $b=n-a$ 1s such that the number of inversions in the array is equal to $x$.

Input format

The first and only line of input contains three space-separated integers - $n$, $a$, and $x$.

Output format

Print space-separated lexicographically smallest array that satisfies the constraints. If there is no valid answer, print $-1$.

Constraints

$1 \leq n\leq 10^6$

$1 \leq x \leq 10^{12}$

$0 \leq a \leq n$

Note

• A pair $(i, j)$ is called an inversion of $A$ if $i < j$ and $A_i > A_j$.
• An array $A$ is said to be lexicographically smaller than array $B$ if there exists an index $t$ such that $A_i = B_i, \forall i < t$ and $A_t < B_t$.