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;
template<class T>inline void init(T&x){
	x=0;char ch=getchar();bool t=0;
	for(;ch>'9'||ch<'0';ch=getchar()) if(ch=='-') t=1;
	for(;ch>='0'&&ch<='9';ch=getchar()) x=(x<<1)+(x<<3)+(ch-48);
	if(t) x=-x;return;
}
const int N=201;
const int MAXN=1e5+10;
const int mod=1e9+7;
typedef long long ll;
template<class T>inline void Inc(T&x,int y){x+=y;if(x>=mod) x-=mod;}
int n,X;
int dp[N][MAXN];
int S[N];
int main()
{
	init(n),init(X);
	for(int i=1;i<=n;++i) init(S[i]);
	sort(S+1,S+1+n);reverse(S+1,S+1+n);
	dp[0][X]=1;
	for(int i=1;i<=n;++i) {
		for(int j=X;~j;--j){
			Inc(dp[i][j%S[i]],dp[i-1][j]);
			Inc(dp[i][j],(ll)(n-i)*dp[i-1][j]%mod);
		}
	}int ans=0;
	for(int i=0;i<=X;++i) Inc(ans,(ll)i*dp[n][i]%mod);
	cout<<ans<<endl;
}
