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 (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"
import "math"

func main(){
	var A, B, syo, ab, amari, ans float64
	var N float64
	var a float64

	fmt.Scan(&N, &A, &B)
	ab = A+B
	// amari = int(N) % int(ab)
	amari = math.Mod(N, ab)
	syo = N / ab

	if A <= amari{
		a = A
	}else {
		a = amari
	}
	// fmt.Println(syo*A, a)
	ans = syo * A + a

	fmt.Println(int(ans))
}