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)

n,a,b = gets.split(' ').map(&:to_i)
#青と赤のボールを何回並べられるか回数を確認
num = n / (a+b)
#青と赤のボールを全部並べられないあまりはいくつか調べる。
extra = n % (a+b)
    
if a == 0
    puts 0
else
    if n <= a
        puts n
    else
        if extra == 0
            puts num * a
        else
            if extra > a
                puts (num * a) + a
            else
                puts (num * a) + extra
            end
        end
    end
end