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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

$N = trim(fgets(STDIN));
$A = trim(fgets(STDIN));
$B = trim(fgets(STDIN));

$numOfBlue = 0;

if ($A !== 0) {
  
  $i = $N / $A + $B ;
  $j = $N % $A + $B ;
  
  if ($j >= $A) {
    
    $k = $A;
  
  } else {
    
    $k = $j;
  }
  
  $numOfBlue = $i*$A + $k;
}

echo  $numOfBlue;