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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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