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Alice and Bob are playing a simple game . They have N integer number and a target number T in common . Either of them independently and randomly picks a number from the N numbers . They win the game if the product of the two picked numbers is strictly greater than the target number T .
You are to calculate the probability that they will win . Assume that each numble is picked with the same probability.
The input consists of multiple test cases . Each test case consists of two lines . The first line contains two integers N (1 ≤ N ≤ 30,000) and T (-1,000,000,000 ≤ T ≤ 1,000,000,000) . The second line contains N integers numbers that Alice and Bob have , each of which will be between -30,000 and 30,000 , inclusive . The last test case is followed by a line containing two zeros.
For each test case , print a line containing the test case number ( beginning with 1 ) followed by the probability of which Alice and Bob will win the game . The probability is printed as a fraction number formatted as “a/b”, where the greatest common divisor of a and b must be 1.
2 0 2 -9 4 5 1 -4 3 -2 0 0
Case 1: 1/2 Case 2: 1/4