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: Wrong Answer)




def main():
    NAB = list(map(int,input().split()))

    b = 0
    if NAB[1] == 0:
        b = 0
    elif NAB[2] == 0:
        b = NAB[1]

    else:
        tm = NAB[0]//(NAB[1]+NAB[2])
        amari = NAB[0] % (NAB[1]+NAB[2])

        b = (tm*NAB[1])+amari



    # cA = NAB[1]
    # cB = NAB[2]
    #
    # for i in range(NAB[0]):
    #
    #     if NAB[1] == 0:
    #         break
    #     if NAB[2] == 0:
    #         b = NAB[1]
    #         break
    #
    #     if cA != 0:
    #         b += 1
    #         cA -= 1
    #     elif cB != 0 and cA == 0:
    #         cB -=1
    #     else:
    #         cA = NAB[1]
    #         cB = NAB[2]
    #
    #         b += 1
    #         cA -= 1


    print(b)



if __name__ == '__main__':
    main()