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

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

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

Input

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

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

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

见题面 Input 部分

见题面 Output 部分

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 $[2, 3, 1]$.