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
MAX = 10**5+1

n,x = map(int,input().split())
s =  list(map(int,input().split()))

fac = [1 for i in range(MAX)]
inv = [1 for i in range(MAX)]
for i in range(2,MAX):
    fac[i] = fac[i-1]*i%MOD
    inv[i] = MOD - inv[MOD%i]*(MOD // i)%MOD

s.sort()
dp = [0 for i in range(x+1)]
for i in range(x+1):dp[i] = (i%s[0])*fac[n-1]%MOD

for i in range(1,n):
    dpp = dp[:]
    for j in range(x+1):
        dpp[j] = (dp[j]+dp[j%s[i]]*inv[i])%MOD
    dp = dpp


print(dp[x])