Problem:
Score : 600 points

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.

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.

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.

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List (sort)
import Data.Maybe (fromJust)

main :: IO ()
main = do
  (n : x : _) <- map read . words <$> getLine :: IO [Int]
  ss <- sort . map read . words <$> getLine :: IO [Int]
  let
    fs = iterate next (0, map (x `mod`) ss ++ [x])
    next = uncurry next'
    next' i = (,) (succ i) . snd . fromJust . foldr step Nothing
      where
        step y Nothing = Just (y, [])
        step y (Just (y', ys')) = Just (y, ((y + i * y') `mod` m) : ys')
  print . head . snd . head . drop n $ fs

m :: Int
m = 10 ^ 9 + 7