Contest: Task: Related: TaskB

Score : $300$ points

There are two $100$-story buildings, called `A`

and `B`

. (In this problem, the ground floor is called the first floor.)

For each $i = 1,\dots, 100$, the $i$-th floor of `A`

and that of `B`

are connected by a corridor.
Also, for each $i = 1,\dots, 99$, there is a corridor that connects the $(i+1)$-th floor of `A`

and the $i$-th floor of `B`

.
You can traverse each of those corridors in both directions, and it takes you $x$ minutes to get to the other end.

Additionally, both of the buildings have staircases. For each $i = 1,\dots, 99$, a staircase connects the $i$-th and $(i+1)$-th floors of a building, and you need $y$ minutes to get to an adjacent floor by taking the stairs.

Find the minimum time needed to reach the $b$-th floor of `B`

from the $a$-th floor of `A`

.

- $1 \leq a,b,x,y \leq 100$
- All values in input are integers.

Input is given from Standard Input in the following format:

$a$ $b$ $x$ $y$

Print the minimum time needed to reach the $b$-th floor of `B`

from the $a$-th floor of `A`

.

2 1 1 5

1

There is a corridor that directly connects the $2$-nd floor of `A`

and the $1$-st floor of `B`

, so you can travel between them in $1$ minute.
This is the fastest way to get there, since taking the stairs just once costs you $5$ minutes.

1 2 100 1

101

For example, if you take the stairs to get to the $2$-nd floor of `A`

and then use the corridor to reach the $2$-nd floor of `B`

, you can get there in $1+100=101$ minutes.

1 100 1 100

199

Using just corridors to travel is the fastest way to get there.