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 fi first
#define se second
#define mp make_pair
#define pb push_back
#define all(x) x.begin(),x.end()
#define dbg(x) cout<<#x<<":"<<x<<endl
typedef long long ll;
typedef pair<ll,ll> P;
typedef pair<ll,P> PP;
ll dp[222][111111];
int main(){
  ll n,x,p=1e9+7;
  cin>>n>>x;
  vector<ll> s(n);
  for(int i=0;i<n;i++)cin>>s[i];
  
  sort(all(s));
  reverse(all(s));
  dp[0][x]=1;
  
  for(int i=0;i<n;i++){
    for(int j=0;j<=x;j++){
	 if(dp[i][j]==0)continue;
	 (dp[i+1][j%s[i]]+=dp[i][j])%=p;
	 (dp[i+1][j]+=dp[i][j]*(n-i-1)%p)%=p;
    }
  }
  ll ans=0;
  for(ll i=0;i<=x;i++){
    (ans+=i*dp[n][i]%p)%=p;
  }
  cout<<ans<<endl;
  return 0;
}
