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 unsigned long long ul;
typedef signed long long ll;
ul over = 1000000007;

mt19937 mt(time(nullptr));
// uniform_int_distribution< int > rand_int(0, 10) // rand[0, 10] inclusive

int main(void)
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed;
  int n, x;
  cin >> n >> x;
  vector< int > s(n);
  for (int i=0; i<n; ++i) cin >> s[i];
  ul ans = 0;
  vector< ul > ai(x+1, 0);
  sort(s.begin(), s.end());
  for (int j=0; j<=x; ++j) ai[j] = j%s[0];
  ul kai = 1;
  for (int i=1; i<n; ++i) {
      kai *= i;
      kai %= over;
      vector< ul > ai2(x+1, 0);
    for (int j=0; j<=x; ++j) {
      ai2[j] = ai[j%s[i]] + ai[j]*i;
      ai2[j] %= over;
    }
    for (int j=0; j<=x; ++j) ai[j] = ai2[j];
  }
  cout << ai[x] << endl;
  return 0;
}
