数论之路慢慢之GCD性质

题目链接

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

题解：

先把i/n-j/m通分，得出（i*m-j*n）/n*m   然后显然可以提出gcd（n，m）因子
就相当于是k*gcd（n，m）/n*m，k为整数，就是个等差数列，然后就相当于去找符合条件的首项，那么由于是绝对值，，不用考虑最小边界的问题，那么容易得出首项为二分之一公差答案
这个题不要忘了化简，，还有必须I64d才能过题

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