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
from collections import defaultdict
N,X=map(int,input().split())
S=[int(i) for i in input().split()]
S=sorted(S,reverse=True)
mod=10**9+7
P=[1]*(N+1)#1/i
for i in range(1,N+1):
    P[i]=pow(i,mod-2,mod)
#print(P)
dd=defaultdict(int)
dd[X]=1
for i in range(N):
    ndd=defaultdict(int)
    for x,p in dd.items():
        ndd[x]+=((1-P[N-i])*p)
        ndd[x]%=mod
        ndd[x%S[i]]+=(P[N-i]*p)
        ndd[x%S[i]]%=mod
    dd=ndd
    #print(dd)
t=1
table=[1]*(N+3)
for i in range(1,N+3):
    t*=i
    t%=mod
    table[i]=t
ans=0
for x,p in dd.items():
    ans+=(x*p*table[N])%mod
    ans%=mod
print(ans)