Modulo Operations

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.

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.

Input

Input is given from Standard Input in the following format:

N X S_1 S_2 \ldots S_{N}

Output

Print the answer.

Examples

Input

2 19 3 7

Output

3

Input

5 82 22 11 6 5 13

Output

288

Input

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

Output

279669259

inputFormat

input are integers.

• 1 \leq N \leq 200
• 1 \leq S_i, X \leq 10^{5}
• S_i are pairwise distinct.

Input

Input is given from Standard Input in the following format:

N X S_1 S_2 \ldots S_{N}

outputFormat

Output

Print the answer.

Examples

Input

2 19 3 7

Output

3

Input

5 82 22 11 6 5 13

Output

288

Input

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

Output

279669259

样例

5 82
22 11 6 5 13

288