Silver Ratio

By Kay Akashi

Problem Statement

You will think of a recursion $a_{n + 2} = pa_{n + 1} + qa_{n}$ $(a_{1} = 1, a_{2} = 1)$.

Given integers $q$ and $d$, find $p$ such that $\lim_{n \to \infty} (\frac{a_{n + 1}}{a_{n}}) = d$. In output, round $p$ to the nearest integer.

Constraints

$1 \leq q, d \leq 1000$.

Input

The input consists of two integers, $q$ and $d$.

Output

Output the answer. Make sure the answer is rounded to the nearest integer.

Examples

33 972

972

891 533

531