A. Increasing and Decreasingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputEach 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).OutputFor 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.ExampleInput
31 4 31 3 3100 200 4Output
1 3 4
-1
100 150 180 200
NoteIn 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.
31 4 31 3 3100 200 4
1 3 4 -1 100 150 180 200 
['constructive algorithms', 'greedy', 'implementation', 'math', '*800']