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>
#define ll long long
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define sort stable_sort
#define all(x) (x).begin(),(x).end()
#define rep(i,x) for (int (i)=(1);(i)<=(x);(i)++)
#define rep2(i,x) for (int (i)=(x);(i)>=(1);(i)--)
#define foreach(it,c) for(__typeof((c).begin()) it=(c).begin();it!=(c).end();it++)
using namespace std;
ll n,m,i,j,dp[205][100005],a[205],mod=1e9+7,ans;
int main()
{
	cin>>n>>m;
	rep(i,n) cin>>a[i];
	sort(a+1,a+n+1);
	rep(i,m) dp[1][i]=i%a[1];
	rep(i,n-1) rep(j,m) dp[i+1][j]=(dp[i][j%a[i+1]]+dp[i][j]*i)%mod;
	cout<<dp[n][m]<<endl;
	return 0;
}