Mrs. Krasteva is known to be very good at guessing the number of people in her class that get a score of 5 on the AP exam. So good in fact that she has always been correct or 1-2 students off. Everyone wants to know her current guess so she has a challenge for you.

She will give you a list of numbers in which each number on the list produces the same remainder ~R~ when dividing the unknown number of people. You will also be given the value of the remainder ~R~. She also says that the number of people is the smallest possible number greater than its divisors which satisfies these conditions.

Find the number of people that score a 5 on the AP exam!

Input Specification

The first line will contain the amount of numbers ~N~ and the shared remainder ~R~

The next ~N~ lines will contain a number ~M~ which produces the remainder ~R~ when dividing the number of people.

Output Specification

Output the smallest number of people that score a 5 on the AP exam ~S \bmod 10^9+7~, satisfying the constraint that the number of people must not be less than ~\min{M}~.

Subtasks

Subtask 1 [40%]

~N\le 10, ~ ~R \le 100, ~ ~M \le 100~

Subtask 2 [30%]

~N\le 25, ~ ~R \le 1000, ~ ~M \le 1000~

Subtask 3 [30%]

~N\le 5, ~ ~R < 10^{10}, ~ ~M < 10^{10}~

Sample Input 1

2 4
5
6

Sample Output 1

34

Sample Input 2

5 10
20 
66
43
34
45

Sample Output 2

1447390