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>
#include<cctype>
using namespace std;
#define rep(i,n) for (int i=0;i<(n);i++)
#define reps(i,n) for (int i=1;i<=(n);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rreps(i,n) for (int i=(n);i>0;i--)
#define all(v) (v).begin(),(v).end()
#define pi 3.1415926535897932384
#define E9 1000000000
#define eps 1e-4
#define pii pair<int,int>
template<class T> inline bool chmin(T &a, T b) {if (a>b) {a = b; return 1;} return 0;};
template<class T> inline bool chmax(T &a, T b) {if (a<b) {a = b; return 1;} return 0;};
typedef long long int ll;
const long long INF = 1LL << 60;

int main(){
  int N, K; cin >> N >> K;
  int A[N]; rep(i,N) cin >> A[i];

  int l=0,r=1000000000;
  while (abs(l-r)>1){
    int x = (l+r)/2;
    ll tmp = 0;
    rep(i,N) tmp += (A[i]-1)/x;
    if (tmp<=K) r = x;
    else l = x;
    // cout << l << " " << r << endl;
  }
  cout << r << endl;
  
  // cout << fixed << setprecision(10);
  
  return 0;
}