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
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MOD = 1e9+7;

int main() {
	int n, x;
	cin >> n >> x;
	vector<int> s(n);
	for (int i = 0; i < n; ++i)
	{
		cin >> s[i];
	}
	sort(s.begin(), s.end(), greater<int>());
	vector<vector<ll> > dp(n+1, vector<ll>(x+1, 0));
	dp[0][x] = 1;
	for (int i = 0; i < n; ++i)
	{
		for (int j = 0; j < x+1; ++j)
		{
			dp[i+1][j] += (n-1-i) * dp[i][j];
			dp[i+1][j] %= MOD;
			dp[i+1][j%s[i]] += dp[i][j];
			dp[i+1][j%s[i]] %= MOD;
		}
	}
	ll ans = 0;
	for (int j = 0; j < x+1; ++j)
	{
		ans += dp[n][j] * j;
		ans %= MOD;
	}
	cout << ans << endl;
	return 0;
}