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():
    mod = 10**9+7
    fact = [1, 1]
    for i in range(2, 300):
        fact.append(fact[-1]*i % mod)

    n, x = map(int, input().split())
    s = sorted(list(map(int, input().split())))[::-1]
    next_dict = {x: fact[n-1]}
    for i in range(n):
        memo = dict()
        inv = pow(n-i-1, mod-2, mod)
        ss = s[i]
        for j, a in next_dict.items():
            memo[j % ss] = (memo.get(j % ss, 0)+a) % mod
        for j, a in memo.items():
            next_dict[j] = (next_dict.get(j, 0)+a*inv) % mod
    ans = 0
    for i, j in memo.items():
        ans = (ans+i*j) % mod
    print(ans)


main()