2017年“嘉杰信息杯” 中国大学生程序设计竞赛全国邀请赛:I— Strange Optimization

题目链接：传送门

Strange Optimization

Bobo is facing a strange optimization problem. Given n,m, he is going to find a real number α such that f(12+α) is maximized, where f(t)=mini,j∈Z|in−jm+t|. Help him!

Note: It can be proved that the result is always rational.

Input

The input contains zero or more test cases and is terminated by end-of-file.

Each test case contains two integers n,m.

• 1≤n,m≤109
• The number of tests cases does not exceed 104.

Output

For each case, output a fraction p/q which denotes the result.

Sample Input

1 1
1 2

Sample Output

1/2
1/4

Note

For the first sample, α=0 maximizes the function.

解题思路：f(t) = 1/Icm(n,m)*2

|i/n-j/m|所能表示的最小值为1/Icm(n,m),令其为p,当t>=p，f(t)=0。当t

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