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: Runtime Error)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');
		int n = int.Parse(input[0]);
		int x = int.Parse(input[1]);
    long mod = 1000000007;
		long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
    Array.Sort(nums);

    long[] answers = new long[x];
    answers[x] = 1;

    for(int i = 0; i < n; i++)
    {
      for(int j = 0; j < x; j++)//余り
      {
        if(answers[j] > 0)
        {
          long memo = answers[j];
          answers[j] *= 2;
          answers[j] %= mod;

          answers[j%nums[i]] += memo;
          answers[j%nums[i]] %= mod;
        }
      }
    }

    
    long answer = 0;
    for(int i = 0; i < x; i++)
    {
      answer += answers[i];
      answer %= mod;
    }
		Console.WriteLine(answer);
	}
}