You are given three integers $$$n$$$, $$$l$$$, and $$$r$$$.

You need to generate an array $$$a$$$ of positive ($$$1 \leq a_i \leq 10^9$$$) integers of length $$$n$$$. Let $$$f(x, y)$$$, for $$$1 \le x \le y \le n$$$, be the bitwise XOR$$$^{\text{∗}}$$$ value $$$a_x \oplus a_{x+1} \oplus \ldots \oplus a_y$$$. You need to make sure that $$$$$$\begin{cases} f(x, y) = 0\quad \text{when }x = l\text{ and }y = r; \text{and}\\ f(x, y) \ne 0\quad \text{when }x \ne l \text{ or } y \ne r. \end{cases}$$$$$$

$$$^{\text{∗}}$$$$$$\oplus$$$ denotes the bitwise XOR operation.

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 three integers $$$n$$$, $$$l$$$, and $$$r$$$ ($$$2 \leq n \leq 4\cdot 10^5$$$, $$$1 \leq l \lt r \leq n$$$).

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

Output

For each test case, print a single line containing $$$n$$$ integers $$$a_1, a_2, \ldots a_n$$$.

We can show that an answer always exists. If there are multiple solutions, print any of them.

Note

In the first test case, $$$f(1, 3) = 9 \oplus 8 \oplus 1 = 0$$$, while all other non-empty subarrays have non-zero bitwise XOR:

$$$f(1, 2) = 9 \oplus 8 = 1 \ne 0$$$,
$$$f(2, 3) = 8 \oplus 1 = 9 \ne 0$$$,
$$$f(1, 1) = 9 \ne 0$$$,
$$$f(2, 2) = 8 \ne 0$$$,
$$$f(3, 3) = 1 \ne 0$$$.

In the second test case, $$$2 \oplus 7 \oplus 5 = 0$$$, while, for example, $$$7 \oplus 5 \oplus 4 = 6 \ne 0$$$.

XOR Array

Examples