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;
typedef long long ll;

#define rep(i,n) for(int i=0; i<n; i++)
#define all(x) (x).begin(),(x).end()
#define INF (1000000000)
#define MOD (1000000007)

ll dp[210][100010];
vector<ll> s;
ll rec(int i,int j){
  if(i==1){
    return dp[i][j] = j%s[i-1];
  }
  if(dp[i][j]>=0)return dp[i][j];
  else return dp[i][j] = ((rec(i-1,j)*(i-1))%MOD+rec(i-1,j%s[i-1]))%MOD;
}
int main(){
  int n,x;
  cin >> n >> x;
  s.assign(n,0);
  rep(i,n){
    cin >> s[i];
  }
  sort(all(s));
  rep(i,210){
    rep(j,100010){
      dp[i][j] = -1;
    }
  }
  cout << rec(n,x) << endl;
}