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 <iostream>
#include <vector>
#include <set>
#include <algorithm>
#include <math.h>
#include <string.h>
#include <map>
#include <numeric>
using namespace std;

const int MOD = 1000000007;
typedef long long ll;

int main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N,X;
  cin>>N>>X;
  vector<int> s(N);
  for(int i=0;i<N;i++){
    cin>>s[i];
  }
  
  vector<vector<ll> > dp(N+1,vector<ll>(X+1,0));
  for(int i=0;i<=X;i++){
    dp[0][i]=i;
  }

  sort(s.begin(),s.end());

  for(int i=0;i<N;i++){
    for(int j=0;j<=X;j++){
      dp[i+1][j] += dp[i][j%s[i]];
      dp[i+1][j] %= MOD;
      dp[i+1][j] += dp[i][j]*i%MOD;
      dp[i+1][j] %= MOD;
    }
  }

  cout<<dp[N][X]<<endl;
}
