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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
	static int n = 0;
	static int[] s;
	static int min = Integer.MAX_VALUE;
	static long[] p = new long[200];
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		int x = sc.nextInt();
		s = new int[n];
		for (int i = 0; i < n; i++) {
			s[i] = sc.nextInt();
			min = Math.min(min, s[i]);
		}
		sc.close();

		p[0] = 1L;
		for (int i = 1; i < 200; i++) {
			p[i] = p[i - 1] * i % 1000000007;
		}
		Arrays.parallelSort(s);

		System.out.println(calc(new HashSet<Integer>(), x));
	}

	static long calc(Set<Integer> set, int x) {
		long ret = 0L;
		int idx = Arrays.binarySearch(s, x);
		if (idx < 0) idx = ~idx;
		for (int i = 0; i < idx; i++) {
			if (!set.contains(s[i])) {
				int nextX = x % s[i];
				if (nextX <= min) {
					ret += nextX % min * p[n - set.size() - 1];
					ret %= 1000000007;
				} else {
					Set<Integer> set2 = new HashSet<Integer>(set);
					set2.add(s[i]);
					ret += calc(set2, nextX);
					ret %= 1000000007;
				}
			}
		}
		return ret;
	}
}