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 <string>
#include <random>
#include <cassert>
#include <cstring>
#include <chrono>

using namespace std;

typedef long long ll;

int main()
{
  const ll mod = 1000 * 1000 * 1000 + 7;
  const int maxValue = 100 * 1000 + 2;
  ll n, x;
  cin >> n >> x;
  vector<ll> s(n);
  for (int i = 0; i < n; ++i) cin >> s[i];
  sort(s.begin(), s.end());
  vector<ll> a(maxValue);

  for (int t = 0; t < maxValue; ++t) a[t] = t % s[0];

  for (ll i = 1; i < n; ++i) {
    vector<ll> b(maxValue);
    for (int t = 0; t < maxValue; ++t) {
      b[t] = (a[t % s[i]] + i * a[t]) % mod;
    }
    a = b;
  }

  cout << a[x] << endl;
  return 0;
}
