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 all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=1<<17,INF=1<<30;

int main(){
    
    int N,X;cin>>N>>X;
    vector<int> A(N);
    for(int i=0;i<N;i++) cin>>A[i];
    sort(all(A));
    
    ll dp[N+1][X+1];
    
    memset(dp,0,sizeof(dp));
    
    for(int j=0;j<X+1;j++) dp[0][j]=j;
    
    for(int i=0;i<N;i++){
        for(int j=0;j<X+1;j++){
            dp[i+1][j]+=dp[i][j]*i;
            dp[i+1][j]%=mod;
        }
        
        for(int j=0;j<X+1;j++){
            dp[i+1][j]+=dp[i][j%A[i]];
            dp[i+1][j]%=mod;
        }
    }
    
    cout<<dp[N][X]<<endl;
}

