Problem: codeforces/2040C
Time limit: 2000 ms, Memory limit: 256 MB

Consider a permutation $ p_1, p_2, \ldots, p_n $ of integers from $ 1 $ to $ n $ . We can introduce the following sum for it :

$$S(p) = \sum_{1 \le l \le r \le n} \min(p_l, p_{l + 1}, \ldots, p_r) $$ 

Let us consider all permutations of length  $ n $  with the maximum possible value of  $ S(p) $ . Output the  $ k $ -th of them in lexicographical order, or report that there are less than  $ k $  of them.  

For example: 

- For the permutation  $ [1, 2, 3] $  the value of  $ S(p) $  is equal to  $ \min(1) + \min(1, 2) + \min(1, 2, 3) + \min(2) + \min(2, 3) + \min(3) = $   $ 1 + 1 + 1 + 2 + 2 + 3 = 10 $  

- For the permutation  $ [2, 4, 1, 3] $  the value of  $ S(p) $  is equal to  $ \min(2) + \min(2, 4) + \min(2, 4, 1) + \min(2, 4, 1, 3) \ + \min(4) + \min(4, 1) +\min(4, 1, 3)\ + \min(1) + \min(1, 3) \ +  \min(3) =  2 + 2 + 1 + 1 + 4 + 1 + 1 + 1 + 1 + 3 = 17 $ .

Input Format

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows.

The only line of each test case contains two integers $ n $ and $ k $ ( $ 1 \le n \le 2 \cdot 10^5 $ ; $ 1 \le k \le 10^{12} $ ) — the length of the permutation and the index number of the desired permutation.

It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10 ^ 5 $ .

Output Format

For each test case, if there are less than $ k $ suitable permutations, print $ -1 $ .

Otherwise, print the $ k $ -th suitable permutation.


Sample Input 1

```
6
3 2
3 3
4 11
4 6
6 39
7 34
```

Sample Output 1

```
1 3 2 
2 3 1 
-1
2 4 3 1 
-1
2 3 4 5 7 6 1
```

Notes

Let us calculate the required sum for all permutations of length $ 3 $ (ordered lexicographically):

 PermutationValue of $ S(p) $  $ [1, 2, 3] $  $ 10 $  $ [1, 3, 2] $  $ 10 $  $ [2, 1, 3] $  $ 9 $  $ [2, 3, 1] $  $ 10 $  $ [3, 1, 2] $  $ 9 $  $ [3, 2, 1] $  $ 10 $ In the first test case, you have to print the second suitable permutation of length $ 3 $ . Looking at the table, we see that it is the permutation $ [1, 3, 2] $ .

In the second test case, you have to print the third suitable permutation of length $ 3 $ . Looking at the table, we see that it is the permutation $ [2, 3, 1] $ .