Craig has a list of ~n~ unique numbers and an infinite number line. For each value ~v_i~ in his list, he highlights all multiples of ~v_i~ on the number line. Once he's done, he asks you what the ~k~th smallest number he highlighted was. Can you help him?

Input

The first line contains two integers, ~n~ and ~k~ (~1 \leq n \leq 15~, ~1 \leq k \leq 10^9~), indicating that there are ~n~ elements in your Craig's list, and he wants to find the ~k~th highlighted number.

The next line contains ~n~ integers, ~v_1, \dots, v_n~ (~1 \leq v_i \leq 10^9~), the elements of Craig's list.

Output

Output the value of the ~k~th smallest number Craig has highlighted.

Example

Input 1

2 8
3 5

Output 1

18

Craig highlighted every 3rd and 5th number, so ~18~ is the ~8~th highlighted number on the number line.

Input 2

3 15
2 3 5

Output 2

21

Input 3

7 10
2 4 6 8 10 12 14

Output 3

20

Input 4

1 1000000000
1000000000

Output 4

1000000000000000000