Problem Statement

Snuke has a blackboard and a set S consisting of N integers.
The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:

• Choose one element from S and remove it.
• Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with $x \bmod {y}$.

There are N! possible orders in which the elements are removed from S.
For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.

Input

Input is given from Standard Input in the following format:
N X
$S_1 S_2 \ldots S_{N}$

Output

Print the answer.

Constraints

• All values in input are integers.
• $1 \leq N \leq 200$
• $1 \leq S_i, X \leq 10^{5}$
• S_i are pairwise distinct.

Sample Input 1

2 19
3 7

Sample Output 1

3

• There are two possible orders in which we remove the numbers from S.
• If we remove 3 and 7 in this order, the number on the blackboard changes as follows: $19 \rightarrow 1 \rightarrow 1$.
• If we remove 7 and 3 in this order, the number on the blackboard changes as follows: $19 \rightarrow 5 \rightarrow 2$.
• The output should be the sum of these: 3.

Sample Input 2

5 82
22 11 6 5 13

Sample Output 2

288

Sample Input 3

10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009

Sample Output 3

279669259

• Be sure to compute the sum modulo 10^{9}+7.

见题面 Input 部分

见题面 Output 部分