Quadratic Equations

Problem code: E4

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Knowing Johnny's mathematical talent, our teacher has prepared a new interesting problem for him, hoping he will enjoy solving it. The problem description is given below.

"There is a rectangular room of length l and width w (l and w are integers). The length and width of the room  fulfill the relation l=Aw+B, where A and B are given integer constants. The room is divided into square cells of unit dimensions. You have observed that, after adding an integer C to the number of cells in the room, the number of cells becomes divisible by the prime number P. Find all the possible values of the width of the room."

 

Input

The first line contains t, the number of test cases (about 10000). Then t test cases follow. Each test case is given in one line containing 4 integers A, B, C and P (2 ? P < 106, 0 < A < P, 0 ? B,C < P).

P is always a prime number.

Output

For each test case, write the result in one line. The first number K is the number of solutions. Then K numbers X1, X2, ...,XK follow (0 ? Xi < P), which are the solutions to the corresponding problems.

Example

Input:
2
1 1 0 2
1 2 2 3

Output:
2 0 1
0

Author: admin
Date Added: 5-06-2009
Time Limit: 3 sec
Source Limit: 50000 Bytes
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