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: Wrong Answer)

# 高橋君は青と赤の 2 色のボールを持っており、これらを一列に並べようとしています。
# 初め、列にボールはありません。根気のある高橋君は、次の操作を 10^100 回繰り返します。
# 列の末尾に、A 個の青いボールを加える。その後、列の末尾に B 個の赤いボールを加える。
# こうしてできる列の先頭から N 個のボールのうち、青いボールの個数はいくつでしょうか。

input = gets.chomp.split
n = input[0].to_i
a = input[1].to_i
b = input[2].to_i

balls = String.new
loop do
    a.times do
        balls += "b"
        break if balls.length >= n
    end
    break if balls.length >= n
    b.times do
        balls += "r"
        break if balls.length >= n
    end
end

puts balls.count("b")