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;


int main(){
	long long int N, X;
	cin >> N >> X;
	vector<long long int >S(N);
	for( size_t i = 0; i < N; i++ ){
		cin >> S[i];
	}
	sort(S.rbegin(), S.rend());
	long long int minv = S[N - 1];
	auto now = map<long long int, long long int>();
	now[X] = 1;
	for( long long int i = 0; i < N; i++ ){
		auto s = S[i];
		auto prev = now;
		now= map<long long int, long long int>();



		for( auto x : prev ){
			now[x.first] += x.second*(N-i-1);
			now[x.first] %= 1000000007LL;
			now[x.first%s] += x.second;
			now[x.first%s] %= 1000000007LL;
		}
	}
	long long int sum = 0;
	for( auto s : now ){
		if( s.first < minv ){
			sum += s.first*s.second;
			sum %= 1000000007LL;
		}
	}
	cout << sum << endl;
}
