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 Python (3.4.3) (judge verdict: Wrong Answer)

import itertools
import math

def create_table(s, x, result={}):
    tmp = []
    ll = len(s)
    for i, a in enumerate(s):
        for b in [x for x in s if x != a]:
            t = [a, b]
            c = s.index(b)
            t += [e for j, e in enumerate(s) if j != c and j != i]
            tmp.append(t)
    for a in tmp:
        kk = x
        for b in a:
            kk %= b
        result[(a[0], a[1])] = kk * math.factorial(ll-2)
    return result

n, x = map(int, input().split())
s = list(map(int, input().split()))
m = 10 ** 9 + 7
if len(s) >= 2:
    mm = create_table(s, x)
    print(sum([a for a in mm.values()]) % m)
else:
    print(x % s[0] % m)