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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <cmath>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <functional>
#include <iomanip>
#include <bitset>
#include <cassert>
using namespace std;
typedef long long ll;

ll mod = 1e9 + 7;
ll dp[203][100003];

int main() {
	int N, X; cin >> N >> X;
	vector<int> s(N);
	for (int i = 0; i < N; i++) {
		cin >> s[i];
	}
	sort(s.rbegin(), s.rend());
	dp[0][X] = 1;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j <= X; j++) {
			dp[i + 1][j%s[i]] += dp[i][j];
			dp[i + 1][j%s[i]] %= mod;
			if (i + 1 != N) {
				dp[i + 1][j] += dp[i][j] * (N - i - 1) % mod;
				dp[i + 1][j] %= mod;
			}
		}
	}
	ll ans = 0;
	for (ll j = 1; j <= X; j++) ans += j*dp[N][j], ans %= mod;
	cout << ans << endl;
	return 0;
}
