Big Division

A theoretical physicist friend is doing research about the "Answer to the Ultimate Question of Life, the Universe, and Everything", he thinks that it is not 42 as suggested by “The Hitchhiker's Guide to the Galaxy” science fiction comedy series; instead he thinks it is the result of dividing the products of two sequences of positive integers A and B!
The task of calculating the product of A and B followed by division turned out to be not as easy as it looks, specially with the sequences being long and the products getting too large very quickly! Even using a modern computer, a straight forward implementation for the calculations may take very long time to complete! And this is where we seek your help as a brilliant computer scientist!

The first line of input contains an integer (1 <= T <= 200), the number of test cases.
T test cases follow, the first line of each test case contains two integers (1 <= N, M<= 110,000), the lengths of sequences A and B respectively. Two lines follow, the first line contains N space separated integers (0 < A0, A1 … An <= 1,000,000), and the second line contains M space separated integers (0 < B0, B1 … Bm <= 1,000,000).

For each test case, print one line containing the result of dividing the product of sequence A by the product of sequence B as a reduced fraction of the format “X / Y” (Notice the single space before and after the fraction sign). X and Y are guaranteed to fit in 32-bit signed integer. A reduced fraction is a fraction such that the greatest common divisor between the nominator and the denominator is 1.

2
3 1
2 4 5
12
2 4
1 15
5 1 7 2

Case #1: 10 / 3
Case #2: 3 / 14

The Third Lebanese Collegiate Programming Contest