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
def main():
    import sys
    input = sys.stdin.readline

    N, x = map(int, input().split())
    S = list(map(int, input().split()))
    S.sort(reverse=True)
    mod = 1000000007

    ans = [0] * (10**5+1)
    ans[x] = 1
    for i, s in enumerate(S):
        for j in range(10**5+1):
            aj = ans[j]
            ans[j%s] = (ans[j%s] + aj)%mod
            ans[j] = (ans[j] + aj * (N-i-2))%mod
    ret = 0
    for k, a in enumerate(ans):
        ret = (ret + (a*k)%mod)%mod
    print(ret)



if __name__ == '__main__':
    main()
