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 Python (3.4.3) (judge verdict: Accepted)

n,a,b=map(int,input().split())
mm=max(a,b)
if a==0:
    print(0)
    exit()
if b==0:
    print(n)
    exit()
xx=n//(a+b)
ans=((xx-1)*a)
baaki=n-((xx-1)*a)-((xx-1)*b)
# print(baaki)
while baaki>0:
    temp=min(baaki,a)
    baaki-=temp
    ans+=temp
    if baaki<=0:
        break
    temp=min(baaki,b)
    baaki-=temp
    if baaki<=0:
        break 
print(ans)