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;

ll dp[202][100010];

signed main(){
    ios::sync_with_stdio(false);
	cin.tie(0);
    cout << fixed << setprecision(20);

    ll n,x;
    cin>>n>>x;
    ll a[n];
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    ll mod = 1e9+7;
    dp[0][x]=1;
    sort(a,a+n,greater<ll>());

    for(int i=0;i<n;i++){
        for(int j=0;j<=x;j++){
            dp[i+1][j%a[i]] += dp[i][j];
            dp[i+1][j%a[i]] %= mod;
            dp[i + 1][j] += dp[i][j] * (n - i - 1); dp[i + 1][j] %= mod;
        }
    }
    ll ans = 0;
    for(ll i=0;i<=x;i++){
        ans += i*dp[n][i];
        ans %= mod;
        //cerr<<i<<" "<<ans<<endl;
    }
    cout<<ans<<endl;
}