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 Common Lisp (SBCL 2.0.3) (judge verdict: Runtime Error)

(let* ((n (read))
       (k (read))
       (a (sort (loop repeat n collect (read)) #'>)))
  (loop while (> k 0)
        do (loop for i from 1
                 while (and (> k i)
                            (> (/ (first a) (+ 1 i))
                               (/ (second a) 2)))
                 finally (if (> k i)
                             (progn
                               (decf k i)
                               (loop with v = (pop a)
                                     repeat (1+ i)
                                     do (push (/ v (1+ i)) a)))
                             (progn
                               (decf k)
                               (let ((v (pop a)))
                                 (push (/ v 2) a)
                                 (push (/ v 2) a)))))
        do (setf a (sort a #'>))
           (print (list k a))
           )
  (format t "~A~%" (ceiling (first a)))
  )