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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;

import java.io.*;

public class Main {

	static int n;
	static long memo[][];
	static int p;
	static int pl[][];
	static pair[] a;
	static int k;

	public static long dp(int msk, int idx) {
		if (idx == n)
			return 0;
		if (memo[msk][idx] != -1)
			return memo[msk][idx];
		long max = k - (idx - Integer.bitCount(msk)) > 0 ? dp(msk, idx + 1) + a[idx].x : dp(msk, idx + 1);

		for (int i = 0; i < p; i++) {
			if (((msk >> i) & 1) == 0) {
				max = Math.max(max, pl[a[idx].y][i] + dp(msk | 1 << i, idx + 1));
			}
		}
		return memo[msk][idx] = max;

	}

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n=Integer.parseInt(st.nextToken());
		int a=Integer.parseInt(st.nextToken());
		int b=Integer.parseInt(st.nextToken());
		int g=n/(a+b);
		int x=n%(a+b);
		System.out.println(g*a+Math.min(a,x));		
	}
	

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class pair {
		int x;
		int y;

		pair(int r, int t) {
			x = r;
			y = t;
		}

		public String toString() {
			return "(" + x + "," + y + ")";
		}

	}
}