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 <algorithm>
#include <iostream>
#include <set>
#include <string>
#include <utility>
#include <vector>

const long long M = 1000000000 + 7;

int main() {
  int n, x;
  std::cin >> n >> x;
  std::vector<int> s(n);
  for (auto &a : s)
    std::cin >> a;
  std::sort(s.begin(), s.end());

  long long f[x + 1];
  for (int xi = 0; xi <= x; ++xi) {
    f[xi] = xi;
  }
  for (int ni = 0; ni < n; ++ni) {
    long long next[x + 1];
    for (int xi = 0; xi <= x; ++xi) {
      next[xi] = (f[xi % s[ni]] + f[xi] * ni) % M;
    }
    for (int xi = 0; xi <= x; ++xi) {
      f[xi] = next[xi];
    }
  }
  std::cout << f[x] << std::endl;
  return 0;
}