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 as dd

N, X = [int(i) for i in input().split()]
sList = [int(i) for i in input().split()]
sList.sort(reverse=True)
mod = 10 ** 9 + 7

dp = dd(int)
dp[X] = 1
for i, s in enumerate(sList):
    new_dp = dd(int)
    for x in dp:
        new_dp[x] += dp[x] * (N - i - 1)
        new_dp[x] %= mod
        new_dp[x % s] += dp[x]
        new_dp[x % s] %= mod
    dp = new_dp

ans = 0
for x in dp:
    ans += x * dp[x]
    ans %= mod

print(ans)
