Subarray permutations
A permutation of length
is an array of integers such that every integer from to (inclusive) appears in it exactly once. For example, is a permutation of length .
A subsegment of an array ] is called good if the subsegment is a permutation of length . For example, the array contains good subsegments: .
You are given two integers and . Find a permutation of length such that it contains exactly good subsegments. Print -1
if no such permutation exists.
Input Format
- The first line contains an integer , denoting the number of test cases. The test cases then follow:
- The first and only line of each test case contains two space-separated integers .
Output Format
For each test case, output a single line containing the answer:
- If no permutation satisfies the given conditions, print
−1
. - Otherwise, print space-separated integers , denoting the elements of the permutation. If there are multiple answers, you can output any of them.
Constraints
- Sum of over all test cases does not exceed .
Subtasks
- Subtask 1 (100 points): Original constraints
Sample Input 1
4
1 1
3 2
4 1
5 3
Sample Output 1
1
1 3 2
-1
5 3 1 4 2
Explanation
Test case : The only permutation of length is , which contains one good subsegment .
Test case : The permutation contains good subsegments: , .
Test case : There is no way to construct a permutation of length which contains one good subsegment.
Test case : The permutation contains good subsegments: . There are other permutations of length having good subsegments
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