Logs

AtCoder

IDabc174_e

Time2000ms

Memory256MB

Difficulty—

We have $N$ logs of lengths $A_1,A_2,\cdots A_N$. We can cut these logs at most $K$ times in total. When a log of length $L$ is cut at a point whose distance from an end of the log is $t$ $(0<t<L)$, it becomes two logs of lengths $t$ and $L-t$. Find the shortest possible length of the longest log after at most $K$ cuts, and print it after rounding up to an integer. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $0 \leq K \leq 10^9$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

2 3
7 9

Output #1

4

*   First, we will cut the log of length $7$ at a point whose distance from an end of the log is $3.5$, resulting in two logs of length $3.5$ each.
*   Next, we will cut the log of length $9$ at a point whose distance from an end of the log is $3$, resulting in two logs of length $3$ and $6$.
*   Lastly, we will cut the log of length $6$ at a point whose distance from an end of the log is $3.3$, resulting in two logs of length $3.3$ and $2.7$.

In this case, the longest length of a log will be $3.5$, which is the shortest possible result. After rounding up to an integer, the output should be $4$.

Input #2

3 0
3 4 5

Output #2

Input #3

10 10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

Output #3

292638192

API Response (JSON)

{
  "problem": {
    "name": "Logs",
    "description": {
      "content": "We have $N$ logs of lengths $A_1,A_2,\\cdots A_N$. We can cut these logs at most $K$ times in total. When a log of length $L$ is cut at a point whose distance from an end of the log is $t$ $(0<t<L)$, i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc174_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ logs of lengths $A_1,A_2,\\cdots A_N$.\nWe can cut these logs at most $K$ times in total. When a log of length $L$ is cut at a point whose distance from an end of the log is $t$ $(0<t<L)$, i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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