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: Runtime Error)

import sys

n,k=map(int,input().split())
a=list(map(int,input().split()))

if k==0:
    print(max(a))
    sys.exit()

def rf(mm):
    if mm==0:
        mm=1
#        return sum(a)
    icnt=0
    for i in range(n):
        icnt+=(a[i]-1)//mm+1
    return icnt

asum=sum(a)
m=asum//(n+k)
um=asum
lm=1
for ii in range(60):
#    print(ii,m)
    if um-lm<10:
        break
    elif rf(m)>(n+k):
        lm=m
        m=(um+lm)//2
    elif rf(m)<(n+k):
        um=m
        m=(lm+um)//2
    elif rf(m)==n+k and rf(m-1)==n+k:
        um=m
        m=(lm+um)//2
    else:
        continue
#        print(m)
#        break

for mi in range(um,lm,-1):
#    print("mi:",mi)
    if rf(mi)==(n+k) and rf(mi-1)>(n+k):
        break
print(mi)