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 Python (3.8.2) (judge verdict: Wrong Answer)

import sys
import math
import time
sys.setrecursionlimit(int(1e6))
if False:
    dprint = print
else:
    def dprint(*args):
        pass

n, k = list(map(int, input().split()))
A = list(map(int, input().split()))
dprint("n, k = ", n, k)
dprint("max(A) = ", max(A))

lx = 0
rx = max(A)
while ((rx-lx) > 1):
    x = (rx + lx) / 2
    dprint("lx, x, rx = ", lx, x, rx)
    kx = 0
    for i in range(len(A)):
        kx += math.ceil(A[i] / x) - 1
    dprint("kx = ", kx)
    if kx <= k:
        dprint(" smoller x")
        rx = x
    else:
        dprint(" cut less, bigger x")
        lx = x

ans = math.ceil(lx)
print(ans)