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 PyPy3 (2.4.0) (judge verdict: Accepted)

#n = int(input())
#s = input()
n,x = map(int,input().split())
da = list(map(int,input().split()))
m = 100010
mod = 1000000007

dp = [0 for i in range(m)]
da.sort()
da.reverse()
dp[x] = 1
for i in range(n):
    for j in range(m):
        if j >= da[i]:
            dp[j%da[i]] += dp[j]
            dp[j] *= n-i-1
            if dp[j] >= mod: dp[j] %= mod
            if dp[j%da[i]] >= mod: dp[j] %= mod
        else:
            dp[j] *= n-i
            if dp[j] >= mod: dp[j]%=mod
ans = 0
for i in range(m):
    ans += dp[i] * i
    if ans >= mod: ans %= mod
print(ans)