Contest Duration: - (local time) (120 minutes) Back to Home
A - Hands /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

100 階建ての建物 A , B があります。 i = 1,\dots, 100 について、建物 Ai 階と Bi 階は廊下で繋がれています。 また、i = 1,\dots, 99 について、建物 Ai+1 階と Bi 階は廊下で繋がれています。 どの廊下も双方向に通行可能で、移動には x 分かかります。 また、A, B どちらの建物にも階段があり、i=1,\dots,99 について、同じ建物の i 階と i+1 階は階段で繋がれています。どの階段も双方向に通行可能で、移動には y 分かかります。

### 制約

• 1 \leq a,b,x,y \leq 100
• 入力はすべて整数

### 入力

a b x y


### 入力例 1

2 1 1 5


### 出力例 1

1


### 入力例 2

1 2 100 1


### 出力例 2

101


### 入力例 3

1 100 1 100


### 出力例 3

199


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.