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: Accepted)

Main(require("fs").readFileSync("/dev/stdin", "utf8"));

function Main(input) {
  input = input.split("\n");
  const [n, k] = input[0].split(" ").map((a) => parseInt(a, 10));
  const a = input[1].split(" ").map((a) => parseInt(a, 10));
  let l = 0, r = 1e9;
  while (r-l > 1) {
    const x = Math.ceil((l+r)/2);
    let now = 0;
    for(let i=0; i<n; i++) {
      now += Math.ceil((a[i])/x) -1;
    }
    if (now <= k) {
      r = x;
    } else {
      l = x;
    }
  }
  console.log(r);
  return;
}