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;
using i64 = long long;
#define rep(i,s,e) for(int (i) = (s);(i) <= (e);(i)++)
#define all(x) x.begin(),x.end()

int N;
vector<i64> s;
i64 X;

i64 dp[202][101010];

const i64 M = 1e9 + 7;

int main() {
  cin >> N;
  cin >> X;
  s.resize(N);
  rep(i,0,N - 1) cin >> s[i]; 

  sort(all(s));
  dp[N][X] = 1;
  for(int i = N - 1;i >= 1;i--) {
    for(i64 x = 0;x < 101010;x++) {
      //use
      (dp[i][x % s[i]] += dp[i + 1][x]) %= M;
      //not use
      (dp[i][x] += dp[i + 1][x] * i % M) %= M;
    }
  }

  i64 ans = 0;

  for(i64 x = 0;x < 101010;x++) {
    (ans += (dp[1][x] * (x % s[0])) % M) %= M;
  }
  cout << ans << endl;
}
