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<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
int mul(int a,int b){return(ll)a*b%mod;}
void inc(int&a,int b){(a+=b)>=mod?a-=mod:0;}
int a[210];
bool cmp(int x,int y){return x>y;}
int f[100010],g[100010];
int main(){
	int n,x,i,j,s;
	scanf("%d%d",&n,&x);
	for(i=1;i<=n;i++)scanf("%d",a+i);
	sort(a+1,a+n+1,cmp);
	f[x]=1;
	for(i=1;i<=n;i++){
		memset(g,0,sizeof(g));
		for(j=0;j<=x;j++){
			if(f[j]){
				inc(g[j],mul(n-i,f[j]));
				inc(g[j%a[i]],f[j]);
			}
		}
		memcpy(f,g,sizeof(g));
	}
	s=0;
	for(i=0;i<a[n];i++)inc(s,mul(i,f[i]));
	printf("%d",s);
}