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 C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll; //10^19 < 9223372036854775807
typedef unsigned long long ull; //10^20 < 18446744073709551615

#define REP(i,n) for(ll i=0;i<ll(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define FOR(i,a,b) for(ll i=a;i<=ll(b);i++)
#define FORD(i,a,b) for(ll i=a;i>=ll(b);i--)
#define FORA(i,I) for(const auto& i:I)
#define ALL(x) x.begin(),x.end() 
#define SIZE(x) ll(x.size()) 

#define MOD 1000000007

int main(void)
{
    ll N, A, B;
    cin >> N >> A >> B;

    ll ans = 0;
    vector<string> boll(N,"");
    REP (i, N+1) {
        REP (j, A) {
            if (i <= N) {
                boll[i++] = 'b';
                ans++;
            }
        }
        REP (k, B) {
            if (i <= N) {
                boll[i++] = 'r';
            }
        }
    }

    cout << ans << endl;

    return 0;
}