Super calculator performs only a single arithmetic operation - multiplication of natural numbers. The upper limit of the range of representations of natural numbers in the calculator is not known. We denote this boundary \textbf{P}. If the result is greater than or equal to the multiplication of \textbf{P} (\textbf{a·b} ≤ \textbf{P}, \textbf{a}, \textbf{b} - factors), the two situations are possible: \begin{enumerate} \item The answer is \textbf{(a·b) mod P} . \item The answer - a random number in the range of valid values (malfunctioning calculator). \end{enumerate} Given the values ​​of the factors (\textbf{a}, \textbf{b}) and result (\textbf{c}). Required to write a program analysis of the calculator, which results in a single number that is generated by the following principle: \begin{enumerate} \item \textbf{0}, if \textbf{c = a·b}; \item \textbf{1}, if the failure occurred; \item the minimum value of \textbf{P}. \end{enumerate} \InputFile The string contains the numbers \textbf{a}, \textbf{b} and \textbf{c} separated by a space, \textbf{a} and \textbf{b} -- factors, \textbf{c} -- the result. \OutputFile This file contains a single number. \textbf{Note}: small Vasya, who dreams of becoming a hacker managed to spy on the length of the line input does not exceed \textbf{15}.