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.

Examples

Input

2 19
3 7


Output

3


Input

5 82
22 11 6 5 13


Output

288


Input

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


Output

279669259
//Insert DP
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int main()
{
	int mod = 1000000007;
	int N, X;
	cin >> N >> X;
	vector<int> s(N, 0);
	for(int i = 0; i < N; i += 1)
	{
		cin >> s[i];
	}
	sort(s.begin(), s.end());
	vector<vector<long>> dp(N + 1, vector<long>(X + 1, 0));
	for(int x = 0; x <= X; x += 1)
	{
		dp[0][x] = x;
	}

	for(int i = 0; i < N; i += 1)
	{
		for(int x = 0; x <= X; x += 1)
		{
			dp[i + 1][x] = (dp[i][x % s[i]] + i * dp[i][x]) % mod; //insert in front of array and in mid of array
		}
	}
	cout << dp[N][X] << endl;
	return 0;
}

