Problem:
Score : 200 points

Problem Statement

Takahashi has many red balls and blue balls. Now, he will place them in a row.

Initially, there is no ball placed.

Takahashi, who is very patient, will do the following operation 10^{100} times:

Place A blue balls at the end of the row of balls already placed. Then, place B red balls at the end of the row.

How many blue balls will be there among the first N balls in the row of balls made this way?

Constraints

1 \leq N \leq 10^{18}

A, B \geq 0

0 < A + B \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the number of blue balls that will be there among the first N balls in the row of balls.

Sample Input 1

8 3 4

Sample Output 1

4

Let b denote a blue ball, and r denote a red ball. The first eight balls in the row will be bbbrrrrb, among which there are four blue balls.

Sample Input 2

8 0 4

Sample Output 2

0

He placed only red balls from the beginning.

Sample Input 3

6 2 4

Sample Output 3

2

Among bbrrrr, there are two blue balls.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main() {
    long long n,a,b,ans=0;
    cin>>n;
    cin>>a;
    cin>>b;
    if(a==0){
        cout<<a;
    }
    else if(b==0){
        cout<<n;
    }
    else{
        ans=a+b;
        if(n%ans==0){
            ans=a*(n/ans);
            cout<<ans;
        }
        else{
            if((n%ans)>a){
                cout<<(a+(a*(n/ans)));
            }
            else{
                cout<<((n%ans)+(a*(n/ans)));
            }
        }
    }
    return 0;
       
}