Increasing and Decreasing
Description
You are given three integers $x$, $y$, and $n$.
Your task is to construct an array $a$ consisting of $n$ integers which satisfies the following conditions:
- $a_1=x$, $a_n=y$;
- $a$ is strictly increasing (i.e. $a_1 < a_2 < \ldots < a_n$);
- if we denote $b_i=a_{i+1}-a_{i}$ for $1 \leq i \leq n-1$, then $b$ is strictly decreasing (i.e. $b_1 > b_2 > \ldots > b_{n-1}$).
If there is no such array $a$, print a single integer $-1$.
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.
The only line of each test case contains three integers $x$, $y$, $n$ ($1 \le x < y \le 1000,3 \le n \le 1000$).
For each test case, output $n$ integers $a_1,a_2,\ldots,a_n$. If there are multiple solutions, print any of them.
If there is no solution, print a single integer $-1$.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.
The only line of each test case contains three integers $x$, $y$, $n$ ($1 \le x < y \le 1000,3 \le n \le 1000$).
Output
For each test case, output $n$ integers $a_1,a_2,\ldots,a_n$. If there are multiple solutions, print any of them.
If there is no solution, print a single integer $-1$.
3
1 4 3
1 3 3
100 200 4
1 3 4
-1
100 150 180 200
Note
In the first test case, $a=[1,3,4]$, which is strictly increasing. Next, $b_1=a_2-a_1=3-1=2$, $b_2=a_3-a_2=4-3=1$, thus $b=[2,1]$, which is strictly decreasing.
In the second test case, there is no array $a$ that satisfies all the conditions above.