J. Elves' Competition

Grandpa Frost is organizing a football tournament for the elves.

He has $2^n$ elves, each uniquely numbered from $1$ to $2^n$. In any match between two elves, the elf with the higher number always wins.

The tournament follows these rules: All elves line up in a row. The first elf competes against the second, the third against the fourth, and so on. In each pair, the losing elf is eliminated, and the winners form a new row by closing ranks. For instance, if the row is $(4,2,3,1)$, elves numbered $2$ and $1$ are eliminated, leaving $(4,3)$. This process repeats $n$ times until only one elf remains, who is declared the winner.

You are a fan of the elf numbered $k$, who is celebrating their $m$th birthday today. As a gift, you need to arrange the initial row of elves so that the elf numbered $k$ wins exactly $m$ matches during the tournament.

Input

The first line contains three integers $n$, $k$, and $m$ ($1\le n\le 15$, $1\le k\le 2^n$, $0\le m\le n$).

Output

If no such initial arrangement exists, output a single integer $-1$.

Otherwise, output $2^n$ numbers — the numbers of the elves in the desired initial row.

If multiple valid arrangements exist, you may output any one of them.

Examples

Note

In the first example, the sequence of rows is: $(1,4,2,3)$ $\to$ $(4,3)$ $\to$ $(4)$.

In the second example, the sequence of rows is: $(4,1,8,2,3,5,6,7)$ $\to$ $(4,8,5,7)$ $\to$ $(8,7)$ $\to$ $(8)$.