Just Random

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)


  Coach Pang and Uncle Yang both love numbers. Every morning they play a game with number together. In each game the following will be done:
  1. Coach Pang randomly choose a integer x in [a, b] with equal probability.
  2. Uncle Yang randomly choose a integer y in [c, d] with equal probability.
  3. If (x + y) mod p = m, they will go out and have a nice day together.
  4. Otherwise, they will do homework that day.
  For given a, b, c, d, p and m, Coach Pang wants to know the probability that they will go out.


  The first line of the input contains an integer T denoting the number of test cases.
  For each test case, there is one line containing six integers a, b, c, d, p and m(0 <= a <= b <= 109, 0 <=c <= d <= 109, 0 <= m < p <= 109).


  For each test case output a single line "Case #x: y". x is the case number and y is a fraction with numerator and denominator separated by a slash ('/') as the probability that they will go out. The fraction should be presented in the simplest form (with the smallest denominator), but always with a denominator (even if it is the unit).

Sample Input

4 0 5 0 5 3 0 0 999999 0 999999 1000000 0 0 3 0 3 8 7 3 3 4 4 7 0

Sample Output

Case #1: 1/3 Case #2: 1/1000000 Case #3: 0/1 Case #4: 1/1



2013 Asia Chengdu Regional Contest