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<iomanip>
//#include<cstdio>
#include<vector>
#include<map>
#include<queue>
#include<algorithm>
#include<cmath>
#include<cassert>
using namespace std;
typedef long long ll;
const int Nmax = 1e5;
const int P = 1e9+7;
int N, X;
int S[Nmax];

int main(){
	cin >> N >> X;
	for(int i=0; i<N; i++) cin >> S[i];

	sort(S, S+N, greater<int>());
	vector<vector<ll> > dp(N+1, vector<ll>(X+1));
	dp[0][X] = 1;
	for(int i=0; i<N; i++){
		for(int j=0; j<=X; j++){
			dp[i][j] %= P;
			dp[i+1][j%S[i]] += dp[i][j];
			dp[i+1][j] += (N-1-i)*dp[i][j]%P;
		}
	}

	ll ans = 0;
	for(int j=0; j<=X; j++){
		ans = (ans+j*dp[N][j])%P;
	}

	cout << ans << endl;

	return 0;
}
