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;
#define LL long long
#define pa pair<int,int>
const int Maxn=210,Maxx=100010;
const int inf=2147483647;
const int mod=1000000007;
int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9')x=(x<<3)+(x<<1)+(ch^48),ch=getchar();
	return x*f;
}
void upd(int&x,int y){x+=y;if(x>=mod)x-=mod;}
int n,a[Maxn],f[Maxn][Maxx];
bool cmp(int x,int y){return x>y;}
int main()
{
	n=read(),a[0]=read();
	for(int i=1;i<=n;i++)a[i]=read();
	sort(a+1,a+1+n,cmp);
	f[0][a[0]]=1;
	for(int i=0;i<n;i++)
	for(int j=1;j<=a[0];j++)
	if(f[i][j])upd(f[i+1][j],(LL)f[i][j]*(n-i-1)%mod),upd(f[i+1][j%a[i+1]],f[i][j]);
	int ans=0;
	for(int i=1;i<a[n];i++)upd(ans,(LL)i*f[n][i]%mod);
	printf("%d",ans);
}