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 M = 1e9 + 7;
int n, k;
vector<int> s;
vector<vector<int>> dp;

int solve(int x, int rem) {
  if (x == n - 1) return rem % s[x];
  int &ret = dp[x][rem];

  if (ret != -1)  return ret;
  ret = 0;

  ret = solve(x + 1, rem % s[x]);
  ret = (ret + 1ll * (n-1-x) * solve(x + 1, rem) % M) % M;
  return ret;
}

int main() {

  ios::sync_with_stdio(false);
  cout.tie(nullptr);
  cin.tie(nullptr);

  cin >> n >> k;
  s.resize(n);
  dp.assign(n, vector<int> (k + 1, -1));
  for (int i = 0; i < n; ++i) {
    cin >> s[i];
  }

  sort(s.begin(), s.end(), greater<int>());
  cout << solve(0, k) << '\n';
}