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;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 1000000000




int main(){
	
	int N;
	cin>>N;
	
	int X;
	cin>>X;
	
	vector<int> S(N);
	for(int i=0;i<N;i++)cin>>S[i];
	
	sort(S.rbegin(),S.rend());
	
	int M = 100000;
	
	vector<vector<int>> dp(N+1,vector<int>(M+1,0));
	dp[0][X] = 1;
	
	for(int i=0;i<N;i++){
		for(int j=0;j<=M;j++){
			dp[i+1][j%S[i]] = mod(dp[i][j]+dp[i+1][j%S[i]]);
			dp[i+1][j] = mod(dp[i+1][j] + mod(dp[i][j]*(N-1-i)));
		}
	}
	
	int ans = 0;
	for(int i=0;i<=M;i++){
		ans = mod(ans + mod(dp.back()[i] * i));
	}
	
	cout<<ans<<endl;
	
    return 0;
}
