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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function Main(input) {
  var tmp = input.trim()
  var N = parseInt(tmp.split(' ')[0])
  var A = parseInt(tmp.split(' ')[1])
  var B = parseInt(tmp.split(' ')[2])

  var stock = { blue: '', red: '' }

  for (var i = 1; i <= A; i++) {
    stock['blue'] = stock['blue'] + 'b'

  }

  var red = ''

  for (var i = 1; i <= B; i++) {
    stock['red'] = stock['red'] + 'r'
  }

  var str = ''
  var j = 0
  var ball = ['blue', 'red']

  while (str.length < N) {
    str = str + stock[ball[j % 2]]
    j = j + 1
  }

  var strSplited = str.split('')
  var result = 0

  for (var k = 0; k < N; ++k) {
    if (strSplited[k] === 'b') {
      result = result + 1
    }
  }

  console.log(result)
  return result
}

Main(require('fs').readFileSync('/dev/stdin', 'utf8'))