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, $7 \oplus 5 \oplus 4 = 6 \ne 0$.