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<string>
using namespace std;
#define ll long long
#define pb push_back
#define endl '\n'
bool cmp(char a, char b){
	return a<b;
}
ll solve(){
	ll n,k;
	cin>>n>>k;
	ll arr[n];
	for(int i=0;i<n;i++){
		cin>>arr[i];
	}
	ll start=0,end=10000000000,mid,mini;
	while((start+1)!=end){
		mid=(start+end)/2;
		//cout<<mid<<endl;
		ll cnt=0,ans=0;
		for(int i=0;i<n;i++){
			if(arr[i]<mid){
				continue;
			}
			else{
				ans+=ceil((arr[i]+0.00)/(mid+0.00))-1;
			}
		}
		if(ans>k) start=mid;
		else {
			mini=mid;
			end=mid;
		}
	}
	cout<<mini;
	return 0;
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	ll t=1;
	//cin>>t;
	while(t--){
		solve();
	}
	return 0;
}