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

\(1 \le N \le 1000 \)

\(1 \le A \le 1000 \)

\( |B| \le 1000 \)

\( 1 \le K \le 10^6 \)