n-th integer divisible by a or b

Given two integers $a$ and $b$. Find the $n$-th positive integer that is divisible by either $a$ or $b$.

Input

Three integers $a,b$ and $n(a,b,n\le 10^9)$.

Output

Print the $n$-th positive integer divisible by either $a$ or $b$. It is known that the answer is no more than $10^9$.

Examples