Codeforces Round #328 (Div. 2)C. The Big Race

C. The Big Race

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Vector Willman and Array Bolt are the two most famous athletes of Byteforces. They are going to compete in a race with a distance of L meters today.

Willman and Bolt have exactly the same speed, so when they compete the result is always a tie. That is a problem for the organizers because they want a winner.

While watching previous races the organizers have noticed that Willman can perform only steps of length equal to w meters, and Bolt can perform only steps of length equal to b meters. Organizers decided to slightly change the rules of the race. Now, at the end of the racetrack there will be an abyss, and the winner will be declared the athlete, who manages to run farther from the starting point of the the racetrack (which is not the subject to change by any of the athletes).

Note that none of the athletes can run infinitely far, as they both will at some moment of time face the point, such that only one step further will cause them to fall in the abyss. In other words, the athlete will not fall into the abyss if the total length of all his steps will be less or equal to the chosen distance L.

Since the organizers are very fair, the are going to set the length of the racetrack as an integer chosen randomly and uniformly in range from 1 to t (both are included). What is the probability that Willman and Bolt tie again today?

Input

The first line of the input contains three integers t, w and b (1 ≤ t, w, b ≤ 5·1018) — the maximum possible length of the racetrack, the length of Willman's steps and the length of Bolt's steps respectively.

Output

Print the answer to the problem as an irreducible fraction . Follow the format of the samples output.

The fraction  (p and q are integers, and both p ≥ 0 and q > 0 holds) is called irreducible, if there is no such integer d > 1, that both p and q are divisible by d.

Sample test(s)

input

10 3 2

output

3/10

input

7 1 2

output

3/7

Note

In the first sample Willman and Bolt will tie in case 1, 6 or 7 are chosen as the length of the racetrack.

题目大意：

      有一个直线赛道，两位运动员每步跑的都是整数，现在在某个地方之后挖一个大坑，运动员会在下一步要踩到之前停下，这时候判断胜者，问有多少几率他们会平局；

解题思路：

     最小公倍数一定是平局，然后每一个平局后也都会有一段平局，长度等于，n,m中小的那个数-1；

     大数；直接用Java过了；

代码：

import java.math.*;
import java.util.Scanner;;
public class cal {

    public static void main(String[] args) {
        Scanner scan=new Scanner(System.in);
        BigInteger t,w,b;
        t=scan.nextBigInteger();
        w=scan.nextBigInteger();
        b=scan.nextBigInteger();
        if(w.compareTo(b)>0)
        {
            BigInteger temp=w;
            w=b;
            b=temp;
        }
        BigInteger temp1=t.mod(w.multiply(b).divide(w.gcd(b)));
        if(temp1.compareTo(w.subtract(BigInteger.ONE))>0)
            temp1=w.subtract(BigInteger.ONE);
        BigInteger num=t.divide(w.multiply(b).divide(w.gcd(b)));
        BigInteger x=w.multiply(num).add(temp1);
        BigInteger i=x.divide(x.gcd(t));
        BigInteger j=t.divide(x.gcd(t));
        System.out.println(i+"/"+j);
    }
}