You are given $N$ ratios in the form of $A$ and $B$ that is represented as $\frac{A}{B}$. The values of $A$ and $B$ are represented as double data type values. The values of $B$ are incorrect. The actual values of $B$ are $B + R$. You know the actual sum of all the ratios that is available in variable $K$.

Note: The true values of $B$, represented as $(B +R)$, are always greater than $0$. Your task is to determine the value of $R$.

Input format

• First line: Two integers $N$ and $col$ denoting the number of ratios and the value $2$ respectively
• Next $N$ lines: Each line contains two double values $A$ and $B$
• Last line: A double value $K$ denoting the sum of all the ratios

Output format

Print the value of $R$. Your answer must contain an absolute or relative error of less than $10^{-6}$.

Constraints

$1 \le N \le 1000$

$1 \le A \le 1000$

$|B| \le 1000$

$1 \le K \le 10^6$