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