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=list(map(int,input().split()))
pr=10**9+7
b={X:1}
S.sort(reverse=1)
def ir(k,v):
    global d
    if k in d:
        d[k]=(d[k]+v)%pr
    else:
        d[k]=v
for i in range(N):
    t=S[i]
    n=N-i-1
    d={}
    for k,v in b.items():
        ir(k%t,v)
        ir(k,v*n)
    b=d
a=0
for k,v in b.items():
    a=(a+k*v)%pr
print(a)