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<vector>
#include<algorithm>
using namespace std;
int N,X;
vector<int>S;
long mod=1e9+7,dp[222][1<<17];
int main()
{
	cin>>N>>X;
	for(int i=0;i<N;i++)
	{
		int s;cin>>s;S.push_back(s);
	}
	sort(S.begin(),S.end());
	dp[0][X]=1;
	for(int i=0;i<N;i++)
	{
		for(int j=0;j<=X;j++)
		{
			if(dp[i][j]==0)continue;
			int k=0;
			for(;k<N;k++)
			{
				if(j<S[k])break;
				(dp[i+1][j%S[k]]+=dp[i][j])%=mod;
			}
			(dp[i+1][j]+=dp[i][j]*(N-k-i)%mod)%=mod;
		}
	}
	long ans=0;
	for(int i=0;i<=X;i++)(ans+=i*dp[N][i])%=mod;
	cout<<ans<<endl;
}