Problem Description

Compute the integral

$\displaystyle{\int_L^R\frac{cx+d}{ax+b}\mathrm{d}x}$

Round the result to $6$ decimal places.

The testdata guarantees that the denominator is not $0$ during the computation and the integral converges.

Input Format

One line containing $6$ real numbers $a,b,c,d,L,R$.

Output Format

One line with the value of the integral, rounded to $6$ decimal places.

1 2 3 4 5 6

2.732937

Hint

$a,b,c,d\in[-10,10]$，$-100\le L<R\le 100$ 且 $R-L\ge1$。

It is guaranteed that each input number has at most one decimal place.

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