﻿ ARC109 A - Hands - Atcoder

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Score : $300$ points

### Problem Statement

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.

### Constraints

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

### Input

Input is given from Standard Input in the following format:

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


### Output

Print the minimum time needed to reach the $b$-th floor of B from the $a$-th floor of A.

### Sample Input 1

2 1 1 5


### Sample Output 1

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.

### Sample Input 2

1 2 100 1


### Sample Output 2

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.

### Sample Input 3

1 100 1 100


### Sample Output 3

199


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