Evirir the dragon has many friends. They have 3 friends! That is one more than the average dragon.

You are given integers $$$n$$$, $$$x$$$, and $$$y$$$. There are $$$n$$$ dragons sitting in a circle. The dragons are numbered $$$1, 2, \ldots, n$$$. For each $$$i$$$ ($$$1 \le i \le n$$$), dragon $$$i$$$ is friends with dragon $$$i - 1$$$ and $$$i + 1$$$, where dragon $$$0$$$ is defined to be dragon $$$n$$$ and dragon $$$n + 1$$$ is defined to be dragon $$$1$$$. Additionally, dragons $$$x$$$ and $$$y$$$ are friends with each other (if they are already friends, this changes nothing). Note that all friendships are mutual.

Output $$$n$$$ non-negative integers $$$a_1, a_2, \ldots, a_n$$$ such that for each dragon $$$i$$$ ($$$1 \le i \le n$$$), the following holds:

Let $$$f_1, f_2, \ldots, f_k$$$ be the friends of dragon $$$i$$$. Then $$$a_i = \operatorname{mex}(a_{f_1}, a_{f_2}, \ldots, a_{f_k})$$$.$$$^{\text{∗}}$$$

$$$^{\text{∗}}$$$The minimum excluded (MEX) of a collection of integers $$$c_1, c_2, \ldots, c_m$$$ is defined as the smallest non-negative integer $$$t$$$ which does not occur in the collection $$$c$$$.

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 first and only line of each test case contains three integers $$$n$$$, $$$x$$$, $$$y$$$ ($$$3 \le n \le 2 \cdot 10^5$$$, $$$1 \le x \lt y \le n$$$).

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

Output

For each test case, output $$$n$$$ space-separated non-negative integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 10^9$$$) on a line that satisfy the condition in the statement. If there are multiple solutions, print any of them. It can be proven that under the problem constraints, a solution with $$$0 \le a_i \le 10^9$$$ always exists.

Note

For the first test case:

$$$i = 1$$$: Dragon $$$1$$$'s friends are dragons $$$2, 3, 5$$$. $$$\operatorname{mex}(a_2, a_3, a_5) = \operatorname{mex}(2, 1, 1) = 0 = a_1$$$, so the condition for dragon $$$1$$$ is satisfied.
$$$i = 2$$$: Dragon $$$2$$$'s friends are dragons $$$1, 3$$$. $$$\operatorname{mex}(a_1, a_3) = \operatorname{mex}(0, 1) = 2 = a_2$$$.
$$$i = 3$$$: Dragon $$$3$$$'s friends are dragons $$$1, 2, 4$$$. $$$\operatorname{mex}(a_1, a_2, a_4) = \operatorname{mex}(0, 2, 0) = 1 = a_3$$$.
$$$i = 4$$$: Dragon $$$4$$$'s friends are dragons $$$3, 5$$$. $$$\operatorname{mex}(a_3, a_5) = \operatorname{mex}(1, 1) = 0 = a_4$$$.
$$$i = 5$$$: Dragon $$$5$$$'s friends are dragons $$$1, 4$$$. $$$\operatorname{mex}(a_1, a_4) = \operatorname{mex}(0, 0) = 1 = a_5$$$.

MEX Cycle

Examples