CF911B 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

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 $ .