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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main 
import ("fmt")

func main(){

  var a int;
  var b int;
  var c int;
  
  var X string;
  var ret int;
  
  fmt.Scanf("%d %d %d", &a, &b, &c );

   
  for; len(X) <=a ;{
      for i :=0; i<b; i++{
          X+= "A"
      }
      for j :=0; j<c; j++{
          X+= "B";
      }
  }
  
  for ind, c:= range X{
        if ind == a{
            break;
        }
        if c == 'A'{
          ret += 1;
        }

  }

    fmt.Println(ret);
}