#arc091c. [arc091_c]LISDL
[arc091_c]LISDL
Problem Statement
Determine if there exists a sequence obtained by permuting that satisfies the following conditions:
- The length of its longest increasing subsequence is .
- The length of its longest decreasing subsequence is .
If it exists, construct one such sequence.
Notes
A subsequence of a sequence is a sequence that can be obtained by extracting some of the elements in without changing the order.
A longest increasing subsequence of a sequence is a sequence with the maximum length among the subsequences of that are monotonically increasing.
Similarly, a longest decreasing subsequence of a sequence is a sequence with the maximum length among the subsequences of that are monotonically decreasing.
Constraints
- All input values are integers.
Input
Input is given from Standard Input in the following format:
Output
If there are no sequences that satisfy the conditions, print -1
.
Otherwise, print integers. The -th integer should be the -th element of the sequence that you constructed.
Sample Input 1
5 3 2
Sample Output 1
2 4 1 5 3
One longest increasing subsequence of this sequence is , and one longest decreasing subsequence of it is .
Sample Input 2
7 7 1
Sample Output 2
1 2 3 4 5 6 7
Sample Input 3
300000 300000 300000
Sample Output 3
-1