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;
const int maxn=3e5;
int a[maxn];
int n;
int P=1e9+7;
long long dp[300][maxn];
long long dfs(int i,int now){
    if(now==0)return 0;
    if(i<1){
        return now;
    }
    if(dp[i][now])return dp[i][now];
    if(now>=a[i])dp[i][now]=(dfs(i-1,now%a[i])+dfs(i-1,now)*(i-1)%P)%P;
    else  dp[i][now]=(dfs(i-1,now)*i)%P;
    return dp[i][now];
}
int main()
{
    int x;
    cin>>n>>x;
    for(int i=1;i<=n;i++)
        cin>>a[i];
    sort(a+1,a+n+1);
    cout<<dfs(n,x);
    /*for(int i=0;i<n;i++){
        cout<<dp[i][x]<<endl;
    }*/
}
