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<iostream>
#include<algorithm>
using namespace std;
const int mod=1000000007;
long dp[201][100001];

int main(){
	int n;
	int x;
	cin >> n >> x;
	int s[n];
	for(int i=0;i<n;i++) cin >> s[i];
	sort(s,s+n);
	reverse(s,s+n);
	
	dp[0][x]=1;
	for(int i=0;i<n;i++){
		for(int j=0;j<=x;j++){
			(dp[i+1][j%s[i]]+=dp[i][j])%mod;
			(dp[i+1][j]+=dp[i][j]*(n-1-i)%mod)%mod;
		}
	}
	long ans=0;
	for(int i=0;i<=x;i++) (ans+=dp[n][i]*i%mod)%mod;
	cout << ans%mod << endl;
	return 0;
}
