Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

2 19
3 7

Sample Output 1

3

There are two possible orders in which we remove the numbers from S.

If we remove 3 and 7 in this order, the number on the blackboard changes as follows: 19 \rightarrow 1 \rightarrow 1.

If we remove 7 and 3 in this order, the number on the blackboard changes as follows: 19 \rightarrow 5 \rightarrow 2.

The output should be the sum of these: 3.

Sample Input 2

5 82
22 11 6 5 13

Sample Output 2

288

Sample Input 3

10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009

Sample Output 3

279669259

Be sure to compute the sum modulo 10^{9}+7.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;
static class Program{
	const int mod=1000000007;
	static int[] s,a,r;
	static long ans=0;
	static void Main(){
		Sc sc=new Sc();
		s=sc.Ia;
		a=sc.Ia;
		r=new int[s[0]+1];
		r[0]=1;
		for(int i = 1;i<=s[0];i++) {r[i]=(r[i-1]*i)%mod;}
		Array.Sort(a);
		for(int i = 0;i<s[0];i++) {
			Fu(1,a[i],s[1],r[s[0]-1]);
		}
		Console.WriteLine("{0}",ans%mod);
	}
	static void Fu(int n,int b,int g,int rr){
		int q=g%b;
		int lb=-1,ub=s[0]-1,mid=0;
		while(ub-lb>1){
			mid=(ub+lb)/2;
			if(a[mid]>q){ub=mid;}
			else{lb=mid;}
		}
		if(ub!=0&&a[ub-1]==b){ub--;}
		if(ub==0){
			ans+=(q*rr)%mod;
			ans%=mod;
		}
		else if(ub==1){
			ans+=((q%a[ub-1])*rr)%mod;
			ans%=mod;
		}
		else{
			for(int i = ub-1;i>=0;i--) {
				Fu(n+1,a[i],q,(int)((rr*Mi(ub))%mod));
			}
		}
		
	}
	static long Mi(long a){
		long b=mod,u=1,v=0;
		while(b>0){
			long t=a/b;
			a-=t*b;a^=b;b^=a;a^=b;
			u-=t*v;u^=v;v^=u;u^=v;
		}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()).Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()).Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
}