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 Ruby (2.3.3) (judge verdict: Accepted)

# ENV[Z = 'RUBY_THREAD_VM_STACK_SIZE'] || exec( { Z => '50000000' },'ruby',$0)
# readlines.map(&:chomp!).map { |e| e.split.map(&:to_i) }
n, a, b = gets.split.map(&:to_i)

if n <= a + b
  if n <= a
    puts n
  else
    puts a
  end
else
  tmp = n / (a + b)
  if (n - (a + b) * tmp) > a
    puts a * tmp + a
  else
    puts a * tmp + (n - (a + b) * tmp)
  end
end