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: Wrong Answer)

#include<stdio.h>
#define i64 long long int
int n;
i64 a[200000];
i64 f(double c)
{
    i64 m=0;
    for(int i=0;i<n;i++)
    {
        m +=(int)(a[i]/c);
    }
    return m;
}
int main()
{
    i64 k,i,y=0;
    double l,m,h;
    scanf("%d %lld",&n,&k);
    for(i=0;i<n;i++)
    {
        scanf("%lld",&a[i]);
         y=y>a[i]?y:a[i];
    }
    if(k==0)i=y;
    else
    {
        l=0.00;
    h=1000000000.00;
    while(l<h)
    {
        m=(l+h)/2;
        i64 k_=f(m);
        if(k_<=k) h=m;
        else l=m+0.0000005;
    }
    i=(int)(l+0.5);
    }
    printf("%lld",i);
    return 0;
}