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;
using nagai = long long;
#define sz(x) int((x).size())

const int N=202;
const int mod=1e9+7;
int mu(int a,int b){
	 return (nagai)a*b%mod;
}
void ad(int&a,int b){
	 if((a+=b)>=mod)a-=mod;
}
int s[N];
const int M=100100;
int dp[N][M];

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n,x;
	cin>>n>>x;
	for(int i=0;i<n;++i)cin>>s[i];
	sort(s,s+n);
	reverse(s,s+n);
	dp[0][x]=1;
	for(int i=0;i<n;++i){
		for(int j=0;j<M;++j){
			ad(dp[i+1][j],mu(dp[i][j],n-i-1));
			ad(dp[i+1][j%s[i]],dp[i][j]);
		}
	}
	int ans=0;
	for(int i=0;i<M;++i){
//		cerr<<i<<' '<<dp[n][i]<<'\n';
		ad(ans,mu(i,dp[n][i]));
	}
	cout<<ans<<'\n';
	return 0;
}

