Find a set $R$ such that:

- All its elements are positive integers.
- It has exactly $N$ elements.
- Non of its elements is greater than $L$.
- Sum of its elements is $S$.
- The total amount of elements $X \in R$, such that $X - 1 \notin R$ is less than 100.

Note: On the second test case the chosen set was: ${3, 4, 5, 7, 9, 10}$

Three integers $N$ ($1 \le N \le 10^9$), $L$ ($1 \le L \le 10^9$), $S$ ($1 \le S \le 10^{18}$).

One line with two integers $A$ and $B$ that represent the number of elements in the set such that the predecessor/successor does not belong to the set, respectively.

One line with $A$ integers sorted increasingly: these are all the elements in the set whose predecessor does not belong to the set.

One line with $B$ integers sorted increasingly: these are all the elements in the set whose successor does not belong to the set.

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

Input

1 1 1

Output

1 1
1
1

Input

6 15 38

Output

3 3
3 7 9
5 7 10