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 N = 200;
const int S = 100005;
const int mo = 1e9 + 7;

int n, x;
int a[N + 5];
int f[N + 5][S + 5];

int main() {
#ifdef Wearry
  freopen("in", "r", stdin);
  freopen("out", "w", stdout);
#endif

  cin >> n >> x;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }

  sort(a, a + n, greater<int>()); 

  f[0][x] = 1;
  for (int i = 0; i < n; ++i) 
    for (int j = 0; j <= x; ++j) if (f[i][j]) {
      f[i + 1][j % a[i]] = (f[i + 1][j % a[i]] + f[i][j]) % mo;
      f[i + 1][j] = (f[i + 1][j] + 1ll * f[i][j] * (n - 1 - i)) % mo;
    }

  int ans = 0;
  for (int i = 0; i <= x; ++i) {
    ans = (ans + 1ll * f[n][i] * i) % mo;
  }
  cout << ans << endl;

  return 0;
}
