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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

int main(){
  int N, K;

  while(std::cin >> N >> K){
    std::vector<int64_t> A(N);
    for(int i = 0; i < N; ++i) std::cin >> A[i];

    auto check =
      [&](double t){
        int64_t m = 0;

        for(auto L : A){
          m += (int64_t)std::ceil(L / t) - 1;
        }
        
        return m <= K;
      };


    double lb = 0.1, ub = 1e9;
    for(int i = 0; i < 100; ++i){
      double mid = (lb + ub) / 2;

      if(check(mid)){
        ub = mid;
      }else{
        lb = mid;
      }
    }

    int ans = std::ceil(lb);

    std::cout << ans << "\n";
  }

  return 0;
}