Array Craft
Description
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.
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 $10^5$.
For each test case, output $n$ space-separated integers $a_1, a_2, \ldots, a_n$ in a new line.
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.
3
2 2 1
4 4 3
6 5 1
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.