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
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
inline void add(long long &x, long long y) {
  x += y;
  if (x >= mod) x -= mod;
}
signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  int n, x;
  cin >> n >> x;
  vector<int> in(n);
  for (int i = 0; i < n; i++) {
    cin >> in[i];
  }
  sort(in.rbegin(), in.rend());
  vector<vector<long long>> dp(n + 1, vector<long long>(x + 1));
  dp[0][x] = 1;
  for (int i = 0; i < n; i++) {
    for (int d = 0; d <= x; d++) {
      add(dp[i + 1][d % in[i]], dp[i][d]);
      add(dp[i + 1][d], dp[i][d] * (n - 1 - i) % mod);
    }
  }
  long long ans = 0;
  for (int d = 0; d <= x; d++) {
    add(ans, d * dp[n][d] % mod);
  }
  cout << ans << endl;
  return 0;
}