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;
using ll=long long;
const int MOD=(int)1e9+7;
const int INF=(int)1e9;
const ll LINF=(ll)1e18;

int main(){
    int n,x;
    cin>>n>>x;
    int s[n];
    for(int i=0;i<n;i++){
        cin>>s[i];
    }
    sort(s,s+n);
    ll dp[2][100001];
    for(int i=0;i<=100000;i++){
        dp[1][i]=i;
    }
    for(int i=0;i<n;i++){
        for(int j=0;j<=100000;j++){
            dp[i%2][j]=(dp[(i+1)%2][j%s[i]]+i*dp[(i+1)%2][j])%MOD;
        }
    }
    cout<<dp[(n-1)%2][x]<<endl;
}
