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.

$^{\text{∗}}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array). $^{\text{†}}$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) \ +$ $\min(1) + \min(1, 3) \ +$ $\min(3) =$ $2 + 2 + 1 + 1 + 4 + 1 + 1 + 1 + 1 + 3 = 17$. $^{\text{‡}}$An array $a$ is lexicographically smaller than an array $b$ if and only if one of the following holds: $a$ is a prefix of $b$, but $a \ne b$; or in the first position where $a$ and $b$ differ, the array $a$ has a smaller element than the corresponding element in $b$.

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.

Note

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 $[2, 3, 1]$.