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 <stdio.h>
#include <stdlib.h>

#define ll long long

int possible(int n, int k, int a[], int l){
    int pieces = 0;
    for(int i=0;i<n;i++){
        pieces += a[i]/l;
        if(a[i]%l==0) pieces -= 1;
    }
    if(pieces<=k) return 1;
    else return 0;
}

int main(){
    int n, k, a[200000];
    scanf("%d%d", &n, &k);
    for(int i=0;i<n;i++) scanf("%d", a+i);
    
    int min = 0, max = (int)1e9 + 1;
    while(max-min>1){
        int middle = (max+min)/2;
        if(possible(n, k, a, middle)){
            max = middle;
        }else{
            min = middle;
        }
    }
    
    printf("%d\n", max);

    return 0;
}