xtu 1268 Strange Optimization 2017年“嘉杰信息杯” 中国大学生程序设计竞赛全国邀请赛（湖南）

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 11 2

Sample Output

1/21/4

Note

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

Source

XTU OnlineJudge

#include<stdio.h>    #define ll __int64  ll gcd(ll a,ll b)  {      return a%b==0?b:gcd(b,a%b);  }    int main()  {      ll a,b;      while(~scanf("%I64d %I64d",&a,&b))      {          printf("1/%I64d\n",2*a*b/gcd(a,b));      }      return 0;  }