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.

St. Chroma

Examples