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 <cstdio>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <numeric>
#include <cmath>

using namespace std;

typedef long long int ll;
typedef pair<int,int> P;

#define all(x) x.begin(),x.end()

const ll mod = 1e9+7;
const ll INF = 1e9;
const ll MAXN = 1e9;

int main()
{
	ll n,x;
	cin>>n>>x;
	vector<ll> s(n);
	for(int i = 0; i < n; i++){
		cin>>s[i];
	}
	sort(all(s));
	reverse(all(s));
	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; j++){
			dp[i+1][j] += dp[i][j]*(n-i-1);
			dp[i+1][j] %= mod;
			dp[i+1][j%s[i]] += dp[i][j];
			dp[i+1][j] %= mod;
		}
	}

	ll ans=0;
	for(int i = 0; i <= x; i++){
		ans += (dp[n][i])*i;
		ans%=mod;
	}
	cout<<ans<<endl;

	return 0;
}