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;
static const int64_t mod=1000000007;
int main(){
  int64_t N,X;cin>>N>>X;
  vector<int64_t>S(N);
  for(int i=0;i<N;i++)
    cin>>S.at(i);
  sort(S.begin(),S.end());
  vector<vector<int64_t>>dp(N,vector<int64_t>(1+X,0));
  for(int j=0;j<=X;j++)
    dp[0][j]=j%S.at(0);
  for(int i=1;i<N;i++)
    for(int j=1;j<=X;j++){
    dp[i][j]=(i*dp[i-1][j]+dp[i-1][j%S[i]])%mod;
    }cout<<dp[N-1][X]<<endl;
  return 0;
}