Make Them Narrow

AtCoder

IDabc361_c

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A$ of length $N$. Freely choose exactly $K$ elements from $A$ and remove them, then concatenate the remaining elements in their original order to form a new sequence $B$. Find the minimum possible value of this: the maximum value of $B$ minus the minimum value of $B$. ## Constraints * All inputs are integers. * $1 \le K < N \le 2 \times 10^5$ * $1 \le A_i \le 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

5 2
3 1 5 4 9

Output #1

2

Consider removing exactly two elements from $A=(3,1,5,4,9)$.

*   For example, if you remove the 2nd element $1$ and the 5th element $9$, the resulting sequence is $B=(3,5,4)$.
    *   In this case, the maximum value of $B$ is $5$ and the minimum value is $3$, so (maximum value of $B$) $-$ (minimum value of $B$) $=2$, which is the minimum possible value.

Input #2

6 5
1 1 1 1 1 1

Output #2

Input #3

8 3
31 43 26 6 18 36 22 13

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Make Them Narrow",
    "description": {
      "content": "You are given a sequence $A$ of length $N$.   Freely choose exactly $K$ elements from $A$ and remove them, then concatenate the remaining elements in their original order to form a new sequence $B$.  ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc361_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $A$ of length $N$.  \nFreely choose exactly $K$ elements from $A$ and remove them, then concatenate the remaining elements in their original order to form a new sequence $B$.  ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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