A16081. Increasing and Decreasing

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:

1. $a_1=x$ , $a_n=y$ ;
2. $a$ is strictly increasing (i.e. $a_1 < a_2 < \ldots < a_n$ );
3. 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 $-1$ .

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.