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

Strange Optimization
Accepted : 89		Submit : 350
Time Limit : 1000 MS		Memory Limit : 65536 KB

 

Strange Optimization

Bobo is facing a strange optimization problem. Given n,m , he is going to find a real number α such that f(1/2+α) is maximized, where f(t)=mini,j∈Z|i/n−j/m+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.

解法：猜的结论...

#include <bits/stdc++.h>
using namespace std;
#define ll long long
int main()
{
    ll n,m;
    while(cin>>n>>m)
    {
        if(n==m)
        {
            cout<<"1/2"<<endl;
        }
        else
        {
            printf("1/%lld\n",n/__gcd(n,m)*m*2);
        }
    }
    return 0;
}