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: Runtime Error)

# -*- coding: utf-8 -*-
"""
Challenge A
"""
import numpy as np
import math as m

    
i = input()
aa = np.array(str.split(i)).astype(int)
#print(aa)
N = aa[0]

char_blue= "b"
char_red = "r"

string_blue= "b"*aa[1]
string_red = "r"*aa[2]

string_tot = (string_blue + string_red)*\
m.ceil(N/(len(string_blue)+len(string_red)))


#print(string_tot)
#print(string_tot[:N])

count_blue = 0

for i in string_tot[:N] :
    if i == 'b':
        count_blue += 1
    
print(count_blue)