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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

func main() {
	io := NewIo(os.Stdin, os.Stdout)
	defer io.Flush()
	n, a, b := io.NextInt(), io.NextInt(), io.NextInt()
	cnt := 0
	q := n / (a + b)
	cnt += q * a
	r := n % (a + b)
	cnt += Min(r, a)
	io.Println(cnt)
}

// Min returns minimum value of inputs
func Min(a ...int) (min int) {
	for i, ai := range a {
		if i == 0 || ai < min {
			min = ai
		}
	}
	return min
}

// Io is I/O object
type Io struct {
	reader    *bufio.Reader
	writer    *bufio.Writer
	tokens    []string
	nextToken int
}

// NewIo returns a new Io instance
func NewIo(r io.Reader, w io.Writer) *Io {
	return &Io{
		reader: bufio.NewReader(r),
		writer: bufio.NewWriter(w),
	}
}

// Flush flushes writer
func (io *Io) Flush() {
	err := io.writer.Flush()
	if err != nil {
		panic(err)
	}
}

// NextLine scans a line from stdin
func (io *Io) NextLine() string {
	var buffer []byte
	for {
		line, isPrefix, err := io.reader.ReadLine()
		if err != nil {
			panic(err)
		}
		buffer = append(buffer, line...)
		if !isPrefix {
			break
		}
	}
	return string(buffer)
}

// Next return a word from stdin
func (io *Io) Next() string {
	for io.nextToken >= len(io.tokens) {
		line := io.NextLine()
		io.tokens = strings.Fields(line)
		io.nextToken = 0
	}
	r := io.tokens[io.nextToken]
	io.nextToken++
	return r
}

// NextInt returns an integer from stdin
func (io *Io) NextInt() int {
	i, err := strconv.Atoi(io.Next())
	if err != nil {
		panic(err)
	}
	return i
}

// Println is a wrapper of fmt.Fprintln
func (io *Io) Println(a ...interface{}) {
	fmt.Fprintln(io.writer, a...)
}