A9759 | Friends and Presents

You have two friends. You want to present each of them several positive integers. You want to present $cnt_{1}$ numbers to the first friend and $cnt_{2}$ numbers to the second friend. Moreover, you want all presented numbers to be distinct, that also means that no number should be presented to both friends.

In addition, the first friend does not like the numbers that are divisible without remainder by prime number $x$ . The second one does not like the numbers that are divisible without remainder by prime number $y$ . Of course, you're not going to present your friends numbers they don't like.

Your task is to find such minimum number $v$ , that you can form presents using numbers from a set $1,2,...,v$ . Of course you may choose not to present some numbers at all.

A positive integer number greater than 1 is called prime if it has no positive divisors other than 1 and itself.

You have two friends. You want to present each of them several positive integers. You want to present $cnt_{1}$ numbers to the first friend and $cnt_{2}$ numbers to the second friend. Moreover, you want all presented numbers to be distinct, that also means that no number should be presented to both friends.

In addition, the first friend does not like the numbers that are divisible without remainder by prime number $x$ . The second one does not like the numbers that are divisible without remainder by prime number $y$ . Of course, you're not going to present your friends numbers they don't like.

Your task is to find such minimum number $v$ , that you can form presents using numbers from a set $1,2,...,v$ . Of course you may choose not to present some numbers at all.

A positive integer number greater than 1 is called prime if it has no positive divisors other than 1 and itself.

Print a single integer — the answer to the problem.