B. Array Craft
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

For an array $$$b$$$ of size $$$m$$$, we define:

  • the maximum prefix position of $$$b$$$ is the smallest index $$$i$$$ that satisfies $$$b_1+\ldots+b_i=\max_{j=1}^{m}(b_1+\ldots+b_j)$$$;
  • the maximum suffix position of $$$b$$$ is the largest index $$$i$$$ that satisfies $$$b_i+\ldots+b_m=\max_{j=1}^{m}(b_j+\ldots+b_m)$$$.

You are given three integers $$$n$$$, $$$x$$$, and $$$y$$$ ($$$x > y$$$). Construct an array $$$a$$$ of size $$$n$$$ satisfying:

  • $$$a_i$$$ is either $$$1$$$ or $$$-1$$$ for all $$$1 \le i \le n$$$;
  • the maximum prefix position of $$$a$$$ is $$$x$$$;
  • the maximum suffix position of $$$a$$$ is $$$y$$$.

If there are multiple arrays that meet the conditions, print any. It can be proven that such an array always exists under the given conditions.

Input

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

For each test case:

  • The only line contains three integers $$$n$$$, $$$x$$$, and $$$y$$$ ($$$2 \leq n \leq 10^5, 1 \le y \lt x \le n)$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases will not exceed $$$10^5$$$.

Output

For each test case, output $$$n$$$ space-separated integers $$$a_1, a_2, \ldots, a_n$$$ in a new line.

Example
Input
3
2 2 1
4 4 3
6 5 1
Output
1 1
1 -1 1 1
1 1 -1 1 1 -1
Note

In the second test case,

  • $$$i=x=4$$$ is the smallest index that satisfies $$$a_1+\ldots +a_i=\max_{j=1}^{n}(a_1+\ldots+a_j)=2$$$;
  • $$$i=y=3$$$ is the greatest index that satisfies $$$a_i+\ldots +a_n=\max_{j=1}^{n}(a_j+\ldots+a_n)=2$$$.

Thus, the array $$$a=[1,-1,1,1]$$$ is considered correct.