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1306 - Solutions to an Equation
  PDF (English) Statistics Forum
Time Limit: 2 second(s) Memory Limit: 32 MB

You have to find the number of solutions of the following equation:

Ax + By + C = 0

Where A, B, C, x, y are integers and x1 ≤ x ≤ x2 and y1 ≤ y ≤ y2.

Input

Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each case starts with a line containing seven integers A, B, C, x1, x2, y1, y2 (x1 ≤ x2, y1 ≤ y2). The value of each integer will lie in the range [-108, 108].

Output

For each case, print the case number and the total number of solutions.

Sample Input

Output for Sample Input

5

1 1 -5 -5 10 2 4

-10 -8 80 -100 100 -90 90

2 3 -4 1 7 0 8

-2 -3 6 -2 5 -10 5

1 8 -32 0 0 1 10

Case 1: 3

Case 2: 37

Case 3: 1

Case 4: 2

Case 5: 1

 


Problem Setter: Jane Alam Jan
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