Given a permutation$^{\text{∗}}$ $p$ of length $n$ that contains every integer from $0$ to $n-1$ and a strip of $n$ cells, St. Chroma will paint the $i$-th cell of the strip in the color $\operatorname{MEX}(p_1, p_2, ..., p_i)$$^{\text{†}}$.

For example, suppose $p = [1, 0, 3, 2]$. Then, St. Chroma will paint the cells of the strip in the following way: $[0, 2, 2, 4]$.

You have been given two integers $n$ and $x$. Because St. Chroma loves color $x$, construct a permutation $p$ such that the number of cells in the strip that are painted color $x$ is maximized.

$^{\text{∗}}$A permutation of length $n$ is a sequence of $n$ elements that contains every integer from $0$ to $n-1$ exactly once. For example, $[0, 3, 1, 2]$ is a permutation, but $[1, 2, 0, 1]$ isn't since $1$ appears twice, and $[1, 3, 2]$ isn't since $0$ does not appear at all.

$^{\text{†}}$The $\operatorname{MEX}$ of a sequence is defined as the first non-negative integer that does not appear in it. For example, $\operatorname{MEX}(1, 3, 0, 2) = 4$, and $\operatorname{MEX}(3, 1, 2) = 0$.

Input

The first line of the input contains a single integer $t$ ($1 \le t \le 4000$) — the number of test cases.

The only line of each test case contains two integers $n$ and $x$ ($1 \le n \le 2 \cdot 10^5$, $0 \le x \le n$) — the number of cells and the color you want to maximize.

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

Output

Output a permutation $p$ of length $n$ such that the number of cells in the strip that are painted color $x$ is maximized. If there exist multiple such permutations, output any of them.

Note

The first example is explained in the statement. It can be shown that $2$ is the maximum amount of cells that can be painted in color $2$. Note that another correct answer would be the permutation $[0, 1, 3, 2]$.

In the second example, the permutation gives the coloring $[0, 0, 0, 4]$, so $3$ cells are painted in color $0$, which can be shown to be maximum.

Samples

7
4 2
4 0
5 0
1 1
3 3
1 0
4 3

1 0 3 2
2 3 1 0
3 2 4 1 0
0
0 2 1
0
1 2 0 3