E - Logs

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.

2 3
7 9

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 $4$.

3 0
3 4 5

5

10 10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

292638192