Favorite Game

AtCoder

IDarc163_b

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence of length $N$: $A=(A_1,A_2,\dots,A_N)$. You can perform the following operation any number of times (possibly zero). * Choose an integer $i$ such that $1 \le i \le N$, and increase or decrease $A_i$ by $1$. Your goal is to make at least $M$ integers $i(3 \le i \le N)$ satisfy $A_1 \le A_i \le A_2$. Find the minimum number of operations required to achieve this goal. ## Constraints * $3 \le N \le 2 \times 10^5$ * $1 \le M \le N-2$ * $1 \le A_i \le 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

3 1
2 3 5

Output #1

2

You can make not less than one integer $i(3 \le i \le N)$ satisfy $A_1 \le A_i \le A_2$ by performing the operation as follows.

*   Choose $i=3$, and decrease $A_i$ by $1$.
*   Choose $i=2$, and increase $A_i$ by $1$.

Since it is impossible to achieve the goal with less than $2$ operation, the answer is $2$.

Input #2

5 2
1 4 2 3 5

Output #2

0

You may already have achieved the goal from the start.

Input #3

8 5
15 59 64 96 31 17 88 9

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Favorite Game",
    "description": {
      "content": "You are given an integer sequence of length $N$: $A=(A_1,A_2,\\dots,A_N)$. You can perform the following operation any number of times (possibly zero). *   Choose an integer $i$ such that $1 \\le i \\le",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc163_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence of length $N$: $A=(A_1,A_2,\\dots,A_N)$. You can perform the following operation any number of times (possibly zero).\n\n*   Choose an integer $i$ such that $1 \\le i \\le...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments