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
from collections import defaultdict


def prepare(n, MOD):
    f = 1
    factorials = [1]
    for i in range(1, n + 1):
        f = f * i % MOD
        factorials.append(f)
    return factorials


n, x = map(int, input().split())
sss = list(map(int, input().split()))
sss.sort(reverse=True)
ms = sss.pop()
MOD = 10 ** 9 + 7
factorials = prepare(n, MOD)
dp = {x: 1}
ans = 0
for i, s in enumerate(sss):
    ndp = defaultdict(lambda: 0)
    k = n - i
    for y, c in dp.items():
        if y < s:
            ndp[y] = (ndp[y] + c * k) % MOD
        else:
            z = y % s
            ndp[y] = (ndp[y] + c * (k - 1)) % MOD
            if z < ms:
                ans = (ans + z * c * factorials[k - 1]) % MOD
            else:
                ndp[z] = (ndp[z] + c) % MOD
    dp = ndp

for y, c in dp.items():
    ans = (ans + (y % ms) * c) % MOD

print(ans)
