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<cstdio>
#include<algorithm>
using namespace std;
int gi(){
	int x=0,w=1;char ch=getchar();
	while ((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
	if (ch=='-') w=0,ch=getchar();
	while (ch>='0'&&ch<='9') x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return w?x:-x;
}
const int mod=1e9+7;
int n,m,a[205],f[205][100005],ans;
bool cmp(int i,int j){return i>j;}
int main(){
	n=gi();m=gi();
	for(int i=1;i<=n;++i)a[i]=gi();
	sort(a+1,a+n+1,cmp);f[0][m]=1;
	for(int i=1;i<n;++i)
		for(int j=0;j<=m;++j){
			f[i][j%a[i]]=(f[i][j%a[i]]+f[i-1][j])%mod;
			f[i][j]=(f[i][j]+1ll*(n-i)*f[i-1][j])%mod;
		}
	for(int j=0;j<=m;++j)f[n][j%a[n]]=(f[n][j%a[n]]+f[n-1][j])%mod;
	for(int j=0;j<=m;++j)ans=(ans+1ll*f[n][j]*j)%mod;
	printf("%d\n",ans);return 0;
}
