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Easy Accuracy: 80.01% Submissions: 40 Points: 2

Given four integers A, B, C, D. A represents the initial position of the geek on the x-axis. In each step, geek can go to X+B or X-B if he is standing at X. The tasks is to check if it is possible for the geek to reach C exactly after D steps. If it is possible to reach C in exactly D steps, then print all distinct possible paths in lexicographical order. Otherwise, print -1

Input:
1. The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
2. The first line of each test case contains four space-separated integers A, B, C, and D.


Output: For each test case, print all distinct possible paths in lexicographical order if it is possible to reach C. Otherwise, print -1.

Constraints:
1. 1 <= T <= 5

2. -10^9 <= A, C <= 10^9
3. 1 <= B <= 10^9
4. 1 <= D <= 12


Example:
Input:

3
2 3 8 4
-3 1 0 3

-3 1 1 3

Output:
2 -1 2 5 8
2 5 2 5 8
2 5 8 5 8
2 5 8 11 8
-3 -2 -1 0
-1


Explanation:
Test case 1: All possible paths are {2, -1, 2, 5, 8}, {2, 5, 2, 5, 8}, {2, 5, 8, 5, 8}, {2, 5, 8, 11, 8}

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