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 int_raw():
    return int(raw_input())

def ss_raw():
    return raw_input().split()

def ints_raw():
    return map(int, ss_raw())

INF = 1 << 29
DIV = 10**9 +7
N,X  = ints_raw()
dp = [{} for x in xrange(X+1)]

Ss = ints_raw()

Ss.sort()


def rec(n,idx):
    if idx == 0:
        return n%Ss[0]
    elif idx in dp[n]:
        return dp[n][idx]
    else:
        ans = (rec(n,idx-1)*idx + rec(n%Ss[idx],idx-1))%DIV
        dp[n][idx]=ans
        return ans

def ans():
    return rec(X,N-1)

print ans()
