You are the Chief Examiner of a unit and you have ~t~ assignments that are needed to be marked. You have ~n~ TAs which mark assignments in parallel. The ~i~-th TA can mark an assignmnt every ~s_i~ minutes. What is the minimum amount of time that it will take to mark all assignments?

Input

The first line will contain integers ~n~ and ~t~. The number of TAs and number of assignments to mark, respectively. The second line contains ~n~ integers, ~s_1,\dots,s_n~, the time it takes for each TA to mark 1 assignment.

Output

Output the minimum time needed to mark every assignment.

Constraints

• ~1 \le n \le 10^5~
• ~1 \le t, s_i \le 10^9~

Example 1

Input

10 123
7 7 4 6 3 8 9 8 5 1

Output

49

Example 2

Input

10 63
8 10 4 6 3 6 9 8 4 5

Output

36