A11533. Two Cakes

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 $x$ !

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.

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.

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 $3$ .