github.com/captn3m0/codechef.git

---
languages_supported:
    - NA
title: E4
category: NA
old_version: true
problem_code: E4
tags:
    - NA
layout: problem
---
###  All submissions for this problem are available. 

### A tutorial for this problem is available [here](/wiki/tutorial-quadratic-equations "here").

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

<pre><b>Input:</b>
2
1 1 0 2
1 2 2 3

<b>Output:</b>
2 0 1
0
</pre>