Problem Statement

You run a shop employing $N$ employees. Each employee comes to work in a fixed cycle. More specifically, starting today, the $i$-th employee repeats the following: working for $A_i$ consecutive days and then taking $A_i$ consecutive days off.

Every day starting today, you will come to work and give a medal to an employee of your choice who comes to work that day. (If no employee comes to work, you will do nothing that day.)

At least how many days does it takes to give every employee $K$ or more medals?

Constraints

• All values in input are integers.
• $1 \le N \le 18$
• $1 \le K \le 10^5$
• $1 \le A_i \le 10^5$

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

Print the answer.