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
n,x=map(int,input().split());s,f,M=sorted(list(map(int,input().split())))[::-1],[1,1],10**9+7
for i in range(2,n):f+=[f[-1]*i%M]
D={x:f[n-1]}
for i, k in enumerate(s):
 m,inv=dict(),pow(n-i-1,M-2,M)
 for j,a in D.items():m[j%k]=(m.get(j%k,0)+a)
 for j,a in m.items():D[j]=(D.get(j,0)+a*inv)%M
print(sum([i*j for i, j in m.items()])%M)