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
mod=10**9+7
N,X=map(int,input().split())
S=[int(i) for i in input().split()]
S.sort(reverse=True)

Factorial=[1]*(N+1)
for i in range(1,N+1):
  Factorial[i]=Factorial[i-1]*(i)%mod
def power(x,y):
  if y==0:
    return 1
  elif y==1:
    return x%mod
  elif y%2==0:
    return power(x,y//2)**2%mod
  else:
    return ((power(x,y//2)**2)*x)%mod
inv=[0]*(N+1)
for i in range(N+1):
  inv[i]=power(i,mod-2)
dp=[[0]*(X+1) for i in range(N+1)]
for x in range(X+1):
  dp[N][x]=x
for i in range(N)[::-1]:
  for x in range(X+1):
    dp[i][x]=dp[i+1][x%S[i]]+(N-i-1)*dp[i+1][x]
    dp[i][x]%=mod
print((dp[0][X])%mod)