#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

int main(){
  int n,k;
  cin>>n>>k;
  vector<ll> a(n);
  int ma=0;
  rep(i,n){
    int A; cin>>A;
    a[i]=A;
    ma=max(ma,A);
  }
  int ng=0, ok=ma;
  while(ok-ng>1){
    ll mid=(ok+ng)/2;
    ll cnt=0;
    rep(i,n){
      cnt+=(a[i]+mid-1)/mid-1;
    }
    if(cnt<=k) ok=mid;
    else ng=mid;
  }
  cout<<ok<<endl;
}

### Prompt

Create a solution in Cpp for the following problem:

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.

Examples

Input

2 3
7 9


Output

4


Input

3 0
3 4 5


Output

5


Input

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


Output

292638192

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

int main(){
  int n,k;
  cin>>n>>k;
  vector<ll> a(n);
  int ma=0;
  rep(i,n){
    int A; cin>>A;
    a[i]=A;
    ma=max(ma,A);
  }
  int ng=0, ok=ma;
  while(ok-ng>1){
    ll mid=(ok+ng)/2;
    ll cnt=0;
    rep(i,n){
      cnt+=(a[i]+mid-1)/mid-1;
    }
    if(cnt<=k) ok=mid;
    else ng=mid;
  }
  cout<<ok<<endl;
}

```