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;
const int N = 204,M = 1e5+5;
const int mod=1e9+7;
int a[N],n,X;
int f[N][M];

int main()
{
	cin >> n >> X;
	for(int i=1;i<=n;i++)cin >> a[i];
	sort(a+1,a+n+1);
	f[n+1][X]=1; 
	for(int i=n;i;i--){
		for(int j=1;j<=X;j++){
			f[i][j%a[i]] += f[i+1][j]; f[i][j%a[i]]%=mod;
			f[i][j] += (long long)f[i+1][j]*(i-1)%mod; f[i][j]%=mod;
		}
	}
	int ans = 0;
	for(int j=1;j<=X;j++){
		ans = ans + (long long)j * f[1][j] %mod;
		ans %= mod;
	}
	cout << ans << endl;
}