Farmer John has received an order for exactly $M$ units of milk ($1 \leq M \leq 1,000$) that he needs to fill right away. Unfortunately, his fancy milking machine has just become broken, and all he has are three milk pails of integer sizes $X$, $Y$, and $M$ ($1 \leq X < Y < M$). All three pails are initially empty. Using these three pails, he can perform any number of the following two types of operations:
- He can fill the smallest pail (of size $X$) completely to the top with $X$ units of milk and pour it into the size-$M$ pail, as long as this will not cause the size-$M$ pail to overflow.
- He can fill the medium-sized pail (of size $Y$) completely to the top with $Y$ units of milk and pour it into the size-$M$ pail, as long as this will not cause the size-$M$ pail to overflow.
Although FJ realizes he may not be able to completely fill the size-$M$ pail, please help him determine the maximum amount of milk he can possibly add to this pail.
Input
The first, and only line of input, contains $X$, $Y$, and $M$, separated by spaces.
Output
Output the maximum amount of milk FJ can possibly add to the size-$M$ pail.
Examples
Input 1
17 25 77
Output 1
76
In this example, FJ fills the pail of size 17 three times and the pail of size 25 once, accumulating a total of 76 units of milk.
Problem credits: Brian Dean