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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;

class D
{
	static int[] Read() => Console.ReadLine().Split().Select(int.Parse).ToArray();
	static void Main()
	{
		var h = Read();
		int n = h[0], x = h[1];
		var s = Read().OrderBy(v => -v).ToArray();

		var dp = new MInt[n + 1, x + 1];
		dp[0, x] = 1;

		for (int i = 1; i <= n; i++)
			for (int j = 0; j <= x; j++)
			{
				var c = dp[i - 1, j];
				if (c.V == 0) continue;

				dp[i, j % s[i - 1]] += c;
				dp[i, j] += c * (n - i);
			}
		Console.WriteLine(Enumerable.Range(0, x + 1).Aggregate((MInt)0, (v, j) => v + j * dp[n, j]));
	}
}

struct MInt
{
	const int M = 1000000007;
	public long V;
	public MInt(long v) { V = (v %= M) < 0 ? v + M : v; }
	public override string ToString() => $"{V}";

	public static implicit operator MInt(long v) => new MInt(v);
	public static MInt operator +(MInt x, MInt y) => x.V + y.V;
	public static MInt operator *(MInt x, MInt y) => x.V * y.V;
}