Consider an infinite sequence $A$ defined as follows: \begin{itemize} \item $A_i = 1, i \le 0$, \item $A_i = A_{ \lfloor i/p \rfloor - x} + A_{ \lfloor i/q \rfloor - y}, i \ge 1$ \end{itemize} You will be given $n, p, q, x$ and $y$. Find the $n$-th element of $A$ (index is $0$-based). \InputFile Five integers $n, p, q, x, y~(0 \le n \le 10^{13}, 2 \le p, q \le 10^9, 0 \le x, y \le 10^9)$. \OutputFile Print the value of $A_n$.