DZY Loves Balls （期望线性性）

   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, Si=1, otherwise Si=0.

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

.

InputThe input consists several test cases. (TestCase≤150)

The first line contains two integers, n, m(1≤n,m≤12)OutputFor 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

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回到题目：

这个题目中，我们可以定义随机变量Xi为：

则有：

X=x1+x2+x3+...

且，E(xi)=p(xi=1)=(m/m+n)(n/m+n-1)

则E(X)=E(X1+X2+X3+...X(m+n-1))

=E(1)+E(2)+...+E(m+n-1)

=mn/(m+n)

真的线性性真的牛逼啊

 

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mn/(m+n)

 

。。。。。。。。