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 math

def cul(i,x):
    if tmp[i][x]==-1:
        tmp[i][x]=( cul(i+1,x)*(N-1-i) + cul(i+1,x%a[i]) )%MOD
    return tmp[i][x]

MOD=10**9+7
N,x=map(int,input().split())

a=list(map(int,input().split()))
a.sort(reverse=True)
tmp= [[-1 for j in range(x+1)] for i in range(N)] + [[j for j in range(x+1)]]

print(cul(0,x))