Description

Little H swears to become the greatest mathematician of the 21st century. He believes that, just like singers, mathematicians need good packaging; otherwise, no matter how capable you are, you cannot get noticed. Therefore, he decides to start with his residence so that at a glance people know a "future great mathematician" lives inside.

For convenience, we set the positive direction of the $x$-axis to the east and the positive direction of the $y$-axis to the north, establishing a Cartesian coordinate system. Little H's house is $100$ Hil long from east to west (Hil is Little H's own unit of length; as for how it converts to "m", nobody knows). The east and west walls are both parallel to the $y$-axis, and the north and south walls are lines with slopes $k_1$ and $k_2$, where $k_1$ and $k_2$ are positive real numbers. There are many lawns at the corners along the north wall and the south wall; each lawn is a rectangle whose sides are parallel to the coordinate axes. The contact points of adjacent lawns lie exactly on the wall, and the $x$-coordinates of these contact points are called the wall's "division points". These division points must be integers from $1$ to $99$.

Little H believes that the combination of symmetry and asymmetry best reflects "mathematical beauty". Therefore, there must be $m$ lawns along the north wall corners and $n$ lawns along the south wall corners, with $m \leq n$. If we denote the sets of division points on the north and south walls by $X_1$ and $X_2$ respectively, then they must satisfy $X_1 \subseteq X_2$, that is, every division point on the north wall must also be a division point on the south wall.

Since Little H does not yet have a large income, he must minimize the construction cost of the lawns, i.e., minimize the total area occupied by the lawns. Can you write a program to help him solve this problem?

Input Format

A single line containing $4$ numbers $k_1$, $k_2$, $m$, $n$. The numbers $k_1$ and $k_2$ are positive real numbers representing the slopes of the north and south walls, accurate to one decimal place. The numbers $m$ and $n$ are positive integers representing the number of lawns along the north wall corners and the south wall corners, respectively.

Output Format

A real number, the minimal total area occupied by the lawns, to one decimal place.

0.5 0.2 2 4

3000.0

Hint

Conventions

○ $2 \leq m \leq n \leq 100$.

○ The distance between the north and south walls is very large; there will be no overlap between lawns near the south wall and those near the north wall.

Translated by ChatGPT 5