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;

long long n,x,v[205],dp[205][100005][2],mod=1e9+7ll;

int main(){

	cin>>n>>x;
	
	for(int i=0;i<n;i++)cin>>v[i];
	sort(v,v+n);
	reverse(v,v+n);
	
	for(long long i=n-1;i>=0;i--){
	    for(int j=0;j<100005;j++){
	        if(i==n-1){
	            dp[i][j][0]=dp[i][j][1]=j%v[i];
                continue;
            }
            
            dp[i][j][1]=(dp[i+1][j%v[i]][1]+dp[i+2][j%v[i]][0])%mod;
            
            dp[i][j][0]=((dp[i][j][1]+dp[i+1][j][0])*(n-i))%mod;
        }
    }

    cout<<(dp[0][x][1]+dp[1][x][0])%mod<<endl;

return 0;
}
