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>
const int INF=1e9,MOD=1e9+7;
const long long LINF=1e18;
using namespace std;
#define int long long
//template
int N;
std::vector<int> v(1000000,LINF),w(1000000);
int dp[201][100005];
int f(int i,int x){
  //cout<<i<<" "<<x<<endl;
  if(dp[i][x]!=-1)return dp[i][x];
  if(i==0)return dp[i][x]=x%v[0];
  int res=0;
  res+=f(i-1,x%v[i]);
  res+=f(i-1,x)*i;
  res%=MOD;
  return dp[i][x]=res;
}

//main
signed main(){
  int X;cin>>N>>X;
  w[0]=1;for(int i=1;i<1000000;i++)w[i]=w[i-1]*i%MOD;
  memset(dp,-1,sizeof(dp));
  for(int i=0;i<N;i++)cin>>v[i];
  sort(v.begin(),v.end());
  cout<<f(N-1,X)<<endl;
  /*
  for(int i=0;i<5;i++){
    for(int j=0;j<20;j++)cout<<dp[i][j]<<" ";cout<<endl;
  }
  */
  //for(int i=0;i<10;i++)cout<<v[i]<<" ";cout<<endl;
}
