Problem:
Score : 500 points

Problem Statement

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

Output

Print an integer representing the answer.

Sample Input 1

2 3
7 9

Sample 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.

Sample Input 2

3 0
3 4 5

Sample Output 2

5

Sample Input 3

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

Sample Output 3

292638192

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

const main = (input) => {
  input = input.trim().split('\n')
  const [, k] = input[0].split(' ').map(Number)
  const logs = input[1].split(' ').map(Number).sort((a, b) => b - a)
  let small = 0
  let big = logs[0]
  let mid = Math.floor((big-small)/2) + small

  let ans = logs[0]

  while (true) {
    if (judge(logs, mid, k)) {
      ans = Math.min(ans, mid)
      const newMid = Math.floor((mid - small) / 2) + small
      if (newMid === mid) break
      big = mid
      mid = newMid
    } else {
      const newMid = Math.floor((big - mid) / 2) + mid
      if (newMid === mid) break
      small = mid
      mid = newMid
    }
  }

  return console.log(ans)
}

const judge = (logs, max, k) => {
  if (logs[0] <= max) return true

  let count = 0
  for (let i=0; i<logs.length; i++) {
    let s = logs[i]
    while (s > max) {
      s -= max
      count++
    }
    if (count > k) return false
  }

  return count <= k

  // const _logs = JSON.parse(JSON.stringify(logs))
  // for (let i=0; i<k; i++) {
  //   if (_logs[0] <= max) return true
  //
  //   if (_logs[0] - max > max) _logs[0] -= max
  //   else _logs.shift()
  // }
  //
  // return (_logs[0] <= max || !_logs.length)
}

process.env.MYTEST ? test() : main(require('fs').readFileSync('/dev/stdin', 'utf8'))