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: Time Limit Exceeded)

a = list(map(int,input().split()))
N = a[0]
A = a[1]  #blue
B = a[2]  #red

blue = 0
red = 0
b = 0
r = 0
flag = 0



for i in range(1, N):
    if flag == 0 and b < A:
        b = b + 1
        blue = blue + 1
        #print(blue)
        #print('b')
    if b == A:
        #blue = blue + 1
        flag = 1
        b = 0
        i -= 1
        #print(blue)
        #print('blue')
    if flag == 1 and r < B:
        r = r + 1
        #print('r')
        #print(r)
    if  r == B:
        flag = 0
        r = 0
        i -= 1
        #print('red')
"""

while blue+red < N:
    if flag == 0 & b<A:
        b += 1
        blue += 1
    if b == A:
        flag = 1
        b = 0
    if flag == 0 & r<B:
        r += 1
        red += 1
    if r == B:
        flag = 0
        r = 0
"""""

print(blue)