Increasing and Decreasing

1000ms

262144K

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 $$$-1$$$.

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 $$$-1$$$.

Sample Input:

Sample Output:

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.

Informação

Provedor Codeforces

Código CF1864A