911B - Two Cakes

B. Two Cakes

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

It's New Year's Eve soon, so Ivan decided it's high time he started setting the table. Ivan has bought two cakes and cut them into pieces: the first cake has been cut into a pieces, and the second one — into b pieces.

Ivan knows that there will be n people at the celebration (including himself), so Ivan has set nplates for the cakes. Now he is thinking about how to distribute the cakes between the plates. Ivan wants to do it in such a way that all following conditions are met:

1. Each piece of each cake is put on some plate;
2. Each plate contains at least one piece of cake;
3. No plate contains pieces of both cakes.

To make his guests happy, Ivan wants to distribute the cakes in such a way that the minimum number of pieces on the plate is maximized. Formally, Ivan wants to know the maximum possible number x such that he can distribute the cakes according to the aforementioned conditions, and each plate will contain at least x pieces of cake.

Help Ivan to calculate this number x!

Input

The first line contains three integers n, a and b (1 ≤ a, b ≤ 100, 2 ≤ n ≤ a + b) — the number of plates, the number of pieces of the first cake, and the number of pieces of the second cake, respectively.

Output

Print the maximum possible number x such that Ivan can distribute the cake in such a way that each plate will contain at least x pieces of cake.

Examples

input

5 2 3

output

1

input

4 7 10

output

3

Note

In the first example there is only one way to distribute cakes to plates, all of them will have 1cake on it.

In the second example you can have two plates with 3 and 4 pieces of the first cake and two plates both with 5 pieces of the second cake. Minimal number of pieces is 3.

题意：给n个盘子，第一份蛋糕a份，第二份蛋糕b份。每个蛋糕的每一块都放在一个盘子上； 每个盘子至少包含一块蛋糕；求出每个盘子至少能放几块蛋糕，让这个数最大。

题解：暴力

#include
using namespace std;
int main()
{
    int n,a,b,ans;
    while(cin>>n>>a>>b)
    {
        ans=0;
        for(int i=1;i