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 all(x) (x).begin(),(x).end()
#define SP <<" "<<
#define MOD 1000000007
#define IINF 1000000000
#define LINF 1000000000000000000

typedef long long LL;
typedef long double LD;

int main(){
  int n,x;
  cin >> n >> x;
  vector<int> s(n);
  for(int i=0;i<n;i++){
    cin >> s[i];
  }
  sort(all(s),greater<int>());
  vector<LL> dp(x+1,0);
  dp[x]=1;
  for(int i=0;i<n;i++){
    LL tmp;
    for(int j=0;j<=x;j++){
      tmp=dp[j];
      dp[j]=dp[j]*(n-i-1)%MOD;
      dp[j%s[i]]=(dp[j%s[i]]+tmp)%MOD;
    }
  }
  LL ans=0;
  for(int i=0;i<=x;i++){
    ans=(ans+dp[i]*i%MOD)%MOD;
  }
  cout << ans << endl;
  return 0;
}
