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.

Examples

Input

2 3
7 9

Output

4

Input

3 0
3 4 5

Output

5

Input

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

Output

292638192

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