Consider an infinite sequence $A$ defined as follows: \begin{itemize} \item $A_0 = 1$, \item $A_i = A_{i/p} + A_{i/q}, i \ge 1$ \end{itemize} You are given $n, p$ and $q$. Find the value of $A_n$. \InputFile Three integers $n, p$ and $q~(0 \le n \le 10^{12}, 2 \le p, q \le 10^9)$. \OutputFile Print the value of $A_n$.