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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(void)
{
	long int n, a, b, set, setNum, remainBall;

	scanf("%ld%ld%ld",&n, &a, &b);
	
	/* 青と赤のボールを1セットとし、n番目までに完全な形で並ぶセット数を数える */
	set = a + b;
	setNum = n / set;
	remainBall = n % set;

	/* n番目のボールが青のとき */
	if (remainBall <= a)
	{
		printf("%ld", a * setNum + remainBall);
	}
	/* n番目のボールが赤のとき */
	else
	{
		printf("%ld", a * setNum + a);
	}

	return 0;
}