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
import sys
input = sys.stdin.readline
n,x = map(int,input().split())
s = list(map(int,input().split()))
s.sort(reverse = True)
mod = 10**9+7

#dp[i][x]:s[i]まででxである場合の数
dp = [[0]*(x+1) for i in range(n+1)]
dp[0][x] = 1
for i,p in enumerate(s):
    for j in range(x+1):
        if dp[i][j] == 0:
            continue
        dp[i+1][j%p] += dp[i][j]
        dp[i+1][j] += dp[i][j]*(n-i-1)
        dp[i+1][j%p] %= mod
        dp[i+1][j] %= mod
res = 0
for i in range(1,x+1):
    res += dp[-1][i]*i
    res %= mod
print(res)