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
#include<iostream>
#include<algorithm>
using namespace std;
const int N=1e5+10,mod=1e9+7;
int n,X,f[N],Ans,g[N],s[N];
int cmp(int a,int b) {return a>b;}
int main()
{
	cin>>n>>X;
	f[X]=1;
	for(int i=1;i<=n;i++) cin>>s[i];
	sort(s+1,s+n+1,cmp);
	for(int i=1,x;i<=n;i++)
	{
		x=s[i];
		for(int j=0;j<=X;j++) g[j]=0;
		for(int j=0;j<=X;j++)
		{
			(g[j%x]+=f[j])%=mod;
			(g[j]+=1ll*f[j]*(n-i)%mod)%=mod;
		}
		for(int j=0;j<=X;j++) f[j]=g[j];		
	}
	for(int j=0;j<=X;j++) (Ans+=1ll*f[j]*j%mod)%=mod;
	cout<<Ans<<endl;
}
