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 n plates 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 1 cake 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.


import java.util.Scanner;

public class a {

	public static void main(String args[])
	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int a=scan.nextInt();
		int b=scan.nextInt();
		//i+j==n 
		int min=Integer.MIN_VALUE;
		for(int i=1;i<=n-1;i++)
		{
			//distribute a dishen on i playes and distribute b dishes on (n-i) plates
			if(i>a || (n-i)>b)
			{
				continue;
			}
			int disha=a/i;
			
			
			int dishb=b/(n-i);
			
			//System.out.println(ansa+" "+ansb);
			min=Math.max(Math.min(disha, dishb),min);
			
		}
		System.out.println(min);
	}
}
