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 int ll;
ll arr[205],dp[205][100005],hell=pow(10,9)+7;
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll n,x;
    cin>>n>>x;
    for(ll i=1;i<=n;i++)
    cin>>arr[i];
    sort(arr+1,arr+n+1);
    for(ll i=0;i<=x;i++)
    dp[0][i]=i;
    for(ll i=1;i<=n;i++)
    for(ll j=0;j<=x;j++)
    dp[i][j]=(dp[i-1][j%arr[i]]+(dp[i-1][j]*(i-1))%hell)%hell;
    cout<<dp[n][x];
}