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 <bits/stdc++.h>
using namespace std;
//#define int long long
int MAX=1000000007;

    int dp[201][100002];
signed main() {
    int n,x;
    cin>>n>>x;
    int s[n];
    for(int i=0;i<n;i++)cin >>s[i];
    fill(dp[0],dp[n+1],int(0));
 
   // cerr<<dp[0][0];
    sort(s,s+n);
  
   long long a;
    dp[n][x]=1;
    for(int i=n-1;i>=0;i--){
        for(int j=0;j<=x;j++){

            a=dp[i][j%s[i]]+dp[i+1][j];a=a%MAX;
            
            dp[i][j%s[i]]=a;
            a=dp[i][j]+long(i)*dp[i+1][j];a=a%MAX;
            
            
             dp[i][j]=a;
        }
    }
    long long ans=0,p;

    for(long long j=0;j<=x;j++){
        p= dp[0][j];
       
        ans=(ans+j*p)%MAX;
   
    }

    cout<<ans;

    return 0;


}
