D - Set

Time limit: 1 s
Memory limit: 256 MiB
Languages: C, C++, Java, Python, ... (details)

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: ${3, 4, 5, 7, 9, 10}$

Input

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

Output

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.

Sample test(s)

Input
1 1 1
Output
1 1 1 1
Input
6 15 38
Output
3 3 3 7 9 5 7 10