Hands

AtCoder

IDarc109_a

Time2000ms

Memory256MB

Difficulty—

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: $a$ $b$ $x$ $y$ [samples]

Samples

Input #1

2 1 1 5

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.

Input #2

1 2 100 1

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.

Input #3

1 100 1 100

Output #3

199

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

API Response (JSON)

{
  "problem": {
    "name": "Hands",
    "description": {
      "content": "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 conne",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc109_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are two $100$\\-story buildings, called `A` and `B`. (In this problem, the ground floor is called the first floor.)\nFor each $i = 1,\\dots, 100$, the $i$\\-th floor of `A` and that of `B` are conne...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments