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>
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define ve vector
#define chmin(x,y) x = min(x,y)
#define chmax(x,y) x = max(x,y)

int main(){
    ll n,k;
    cin >> n >> k;
    ve<ll> a(n);
    rep(i,n) cin >> a[i];
    sort(a.begin(), a.end());
    ll l = 0, r = a[n-1];
    while(r-l>1){
        ll x = (l+r)/2;
        ll cnt=0;
        rep(i,n){
            cnt += (a[i]+x-1)/x-1;
        }
        if(cnt <= k)r=x;
        else l = x;
    }
    cout << r << endl;
    return 0;
}