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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
const int nax = 2e5 + 10;
int n, k;
int a[nax];


int main () {
    cin.tie(0)->sync_with_stdio(false);
    cin >> n >> k;

    for (int i = 1 ; i <= n ; ++ i) {
        cin >> a[i];
    }

    int l = 0, r = 1e9;
    int ans = -1;

    while (l <= r) {
        int mid = l + r >> 1;
        long long tot = 0;

        for (int i = 1 ; i <= n ; ++ i) {
            tot += max(0, (a[i] - 1) / mid);
        }

        if (tot <= k) {
            ans = mid;
            r = mid - 1;
        } else l = mid + 1;
    }

    assert(ans != -1);
    cout << ans << '\n';
}