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: Time Limit Exceeded)

def pans(num)
  puts num
  exit
end

N, A, B = gets.chomp.split.map(&:to_i)
i = 1
ans = Hash.new(0)
cnt = 0

while true
  if i%2 == 1 #青ターン
    for k in 1..A
      ans["青"] += 1
      cnt += 1
      pans(ans["青"]) if cnt == N
    end
  else #赤ターン
    for k in 1..B
      ans["赤"] += 1
      cnt += 1
      pans(ans["青"]) if cnt == N
    end
  end
  i += 1
end