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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

# coding: utf-8
import sys
#from operator import itemgetter
sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read
#from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
import math
#from itertools import product, accumulate, combinations, product
#import bisect
#import numpy as np
#from copy import deepcopy
#from collections import deque

INF = 1 << 50


def run():
    N, K = map(int, sysread().split())
    A = list(map(int, sysread().split()))

    l = 0
    r = 10**9
    eps = 1e-8
    while int(l) != int(r):
        test = (l + r) / 2
        sum = 0
        for a in A:
            val1 = a / test
            val2 = a // test
            if val1 == val2:
                sum += val2 - 1
            else:
                sum += val2
        if sum > K:
            l = test
        elif a < K:
            r = test
        else:# sum == K
            r = test
    if int(l) == 0:
        print(1)
        return
    if int(l) == l:
        sum = 0
        for a in A:
            sum += (a - eps) // int(l)
        if sum == K:
            print(int(l))
            return

    print(int(l)+1)

if __name__ == "__main__":
    run()