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DZY Loves Balls

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1172    Accepted Submission(s): 682


Problem Description
There are $n$ black balls and $m$ white balls in the big box.

Now, DZY starts to randomly pick out the balls one by one. It forms a sequence $S$. If at the $i$-th operation, DZY takes out the black ball, $S_i=1$, otherwise $S_i=0$.

DZY wants to know the expected times that '01' occurs in $S$.
 

Input
The input consists several test cases. ($TestCase\leq 150$)

The first line contains two integers, $n$, $m(1\leq n,m\leq 12)$
 

Output
For each case, output the corresponding result, the format is $p/q$($p$ and $q$ are coprime)
 

Sample Input
1 1 2 3
 

Sample Output
1/2 6/5
 

Hint
Case 1: S='01' or S='10', so the expected times = 1/2 = 1/2
Case 2: S='00011' or S='00101' or S='00110' or S='01001' or S='01010'
or S='01100' or S='10001' or S='10010' or S='10100' or S='11000',
so the expected times = (1+2+1+2+2+1+1+1+1+0)/10 = 12/10 = 6/5
 

Source
 

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