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 mod = 1e9 + 7;

void add(int &x,int y) {
  x += y;
  if (x >= mod) x -= mod;
}

int mul(int x,int y) {
  return (long long) x * y % mod;
}

int main() {
  ios_base::sync_with_stdio(false);
  int n, x;
  cin >> n >> x;
  vector<int> a(n);
  for (int i = 0; i < n; ++i) cin >> a[i];
  sort(a.begin(), a.end());
  vector<int> f(x + 1);
  f[x] = 1;
  for (int i = n - 1; i >= 0; --i) {
    vector<int> nf(x + 1);
    for (int j = 0; j <= x; ++j) {
      add(nf[j % a[i]], f[j]);
      add(nf[j], mul(i, f[j]));
    }
    f.swap(nf);
  }
  int ans = 0;
  for (int i = 0; i <= x; ++i) {
    add(ans, mul(i, f[i]));
  }
  cout << ans << '\n';
}
