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 $$A_t < B_t$$.