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
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
	Scanner sc = new Scanner(System.in);
	
	public static void main(String[] args) {
		Main m = new Main();
		m.run();
	}
	
	long mod = 1_000_000_000 + 7;
	void run() {
		int n = sc.nextInt();
		int x =  sc.nextInt();
		
		int s[] = new int[n];
		for(int i =0 ; i < n;i++) {
			s[i] = sc.nextInt();
		}
		
		Arrays.sort(s);
		
		long res = rec(s,n-1,x);
		System.out.println(res);
	}
	Map<String,Long> memo = new HashMap<String,Long>();
	
	long rec(int[] s, int t, int now){
		if(now ==0 ) {
			return 0;
		}
		String key = t+"_"+now;
		if(memo.containsKey(key)) {
			return memo.get(key);
		}
		if(t == -1) {
			return now;
		}
		long res = 0 ;
		
		if(s[t] <= now) {
			res += rec(s, t-1, now % s[t]) % mod;
			res += rec(s, t-1, now) * t%mod;
		}else {
			res += rec(s, t-1, now) * (t+1)%mod;
		}
		
		res = res%mod;
		memo.put(key,res);
		return res ;
	}
	
}