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;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=1LL<<61;

int main() {
  ll n,x;
  cin >> n >> x;
  vec a(n);
  for(ll i=0;i<n;i++) cin >> a[i];
  sort(a.begin(),a.end());
  mat dp(n,vec(x+1,0));
  for(ll i=0;i<=x;i++)  dp[0][i]=i%a[0];
  for(ll i=1;i<n;i++) {
    for(ll j=0;j<x+1;j++) {
      dp[i][j]=(dp[i-1][j%a[i]]+i*dp[i-1][j]%mod)%mod;
    }
  }
  cout << dp[n-1][x] << endl;
}