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 ll = long long;
#define rep(i, m, n) for (int i = m; i < n; ++i)
const int MOD = 1000000007;
template<class T> void add(T &a, T b) { a = (a + b) % MOD; }

int main() {
  int N, X;
  cin >> N >> X;
  vector<int> S(N);
  rep(i, 0, N) cin >> S[i];
  sort(S.begin(), S.end());
  vector<vector<ll>> dp(N+1,vector<ll>(X+1));
  rep(i, 0, X+1) dp[0][i] = i;
  rep(i, 0, N) rep(j, 0, X+1) {
    add(dp[i+1][j], dp[i][j%S[i]] + i * dp[i][j]);
  }
  cout << dp[N][X] << endl;
  return 0;
}
