Walk and Teleport

AtCoder

IDarc067_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ towns on a line running east-west. The towns are numbered $1$ through $N$, in order from west to east. Each point on the line has a one-dimensional coordinate, and a point that is farther east has a greater coordinate value. The coordinate of town $i$ is $X_i$. You are now at town $1$, and you want to visit all the other towns. You have two ways to travel: * Walk on the line. Your _fatigue level_ increases by $A$ each time you travel a distance of $1$, regardless of direction. * Teleport to any location of your choice. Your fatigue level increases by $B$, regardless of the distance covered. Find the minimum possible total increase of your fatigue level when you visit all the towns in these two ways. ## Constraints * All input values are integers. * $2≤N≤10^5$ * $1≤X_i≤10^9$ * For all $i(1≤i≤N-1)$, $X_i<X_{i+1}$. * $1≤A≤10^9$ * $1≤B≤10^9$ ## Input The input is given from Standard Input in the following format: $N$ $A$ $B$ $X_1$ $X_2$ $...$ $X_N$ [samples]

Samples

Input #1

4 2 5
1 2 5 7

Output #1

11

From town $1$, walk a distance of $1$ to town $2$, then teleport to town $3$, then walk a distance of $2$ to town $4$. The total increase of your fatigue level in this case is $2×1+5+2×2=11$, which is the minimum possible value.

Input #2

7 1 100
40 43 45 105 108 115 124

Output #2

84

From town $1$, walk all the way to town $7$. The total increase of your fatigue level in this case is $84$, which is the minimum possible value.

Input #3

7 1 2
24 35 40 68 72 99 103

Output #3

12

Visit all the towns in any order by teleporting six times. The total increase of your fatigue level in this case is $12$, which is the minimum possible value.

API Response (JSON)

{
  "problem": {
    "name": "Walk and Teleport",
    "description": {
      "content": "There are $N$ towns on a line running east-west. The towns are numbered $1$ through $N$, in order from west to east. Each point on the line has a one-dimensional coordinate, and a point that is farthe",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc067_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ towns on a line running east-west. The towns are numbered $1$ through $N$, in order from west to east. Each point on the line has a one-dimensional coordinate, and a point that is farthe...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments