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>
#define fi first
#define se second
#define bug cout<<"--------------"<<endl
using namespace std;
typedef long long ll;
const double PI=acos(-1.0);
const double eps=1e-6;
const ll inf=1e18;
const int mod=1e9+7;
const int maxn=1e5+10;
int n,x;
int a[maxn];
ll dp[210][maxn];
int cmp(int a,int b){
    return a>b;
}
int main(){
    ios::sync_with_stdio(false);
    cin>>n>>x;
    for(int i=1;i<=n;i++){
        cin>>a[i];
    }
    sort(a+1,a+n+1,cmp);
    dp[0][x]=1;
    for(int i=1;i<=n;i++){
        for(int j=0;j<=x;j++){
            (dp[i][j%a[i]]+=dp[i-1][j])%mod;
            (dp[i][j]+=dp[i-1][j]*(n-i)%mod)%mod;
        }
    }
    ll ans=0;
    for(int j=0;j<=x;j++){
        ans=(ans+dp[n][j]*j%mod)%mod;
    }
    cout<<ans<<endl;
	return 0;
}
