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: Accepted)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		long X = long.Parse(str[1]);
		long mod = 1000000007;
		var A = new List<long>();
		string[] str2 = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A.Add(long.Parse(str2[i]));
		}
		A.Sort((x,y)=>y.CompareTo(x));
		long[,]D = new long[N+1,X+1];
		D[0,X] = 1;
		for(var i=0;i<N;i++){
			for(var j=0;j<=X;j++){
				long j2 = j%A[i];
				if(j>0){
					D[i+1,j2] = (D[i+1,j2] + D[i,j]) % mod;
				}
				D[i+1,j] = (D[i+1,j] + D[i,j] * (N-1-i)) % mod;
			}
		}
		long ans = 0;
		for(var j=0;j<=X;j++){
			ans = (ans + D[N,j] * j) % mod;
		}
		Console.WriteLine(ans);
	}
}