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
#a,b,c = [int(i) for i in input().split()]

import sys
input = sys.stdin.readline

MOD = 10**9+7

n,x = [int(i) for i in input().split()]
s = [int(i) for i in input().split()]
s.sort(reverse=True)

ans = [0]*(x+1)
ans[x] = 1

#print(s)
for i, ss in enumerate(s):
    bairitu = n-i-1
#    print(bairitu)
    for j,xx in enumerate(ans):
#        print(j,xx)
        ans[j] = (xx*bairitu)%MOD
        ans[j%ss] = (ans[j%ss]+xx)%MOD

#    print(ans)

res=0
for j,xx in enumerate(ans):
    res += j*xx 
    res = res%MOD

print(res)



        