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>
#define ll long long
#define N 210
#define mo 1000000007
#define X 100010
using namespace std;
template <typename T> void read(T &x){
	x=0;char c=getchar();int fh=1;
	while (!isdigit(c)){if (c=='-')fh=-1;c=getchar();}
	while (isdigit(c))x=x*10+c-'0',c=getchar();
	x*=fh;
}
int n,x,a[N],g[X],dp[N][X],ansn;
void add(int &x,int y){x+=y;if (x>=mo) x-=mo;}
int main(){
	read(n);read(x);
	for (int i=1;i<=n;i++) read(a[i]);
	sort(a+1,a+n+1);
	g[0]=0;
	for (int j=1;j<=x;j++){
		g[j]=g[j-1];
		while (j>=a[g[j]+1]&&g[j]+1<=n) g[j]++;
	}
	dp[0][x]=1;
	for (int i=0;i<n;i++){
		for (int j=0;j<=x;j++){
			if (dp[i][j]){
				for (int k=1;k<=g[j];k++)add(dp[i+1][j%a[k]],dp[i][j]);
				add(dp[i+1][j],1ll*dp[i][j]*(n-g[j]-i)%mo);
			}
		}
	}
	for (int j=0;j<=x;j++) add(ansn,1ll*dp[n][j]*j%mo);
	cout<<ansn<<endl;
	return 0;
}