CF1864A 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.