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 <iostream>
#include <algorithm>
#include <vector>

const long long int MOD = 1000000007;

int main()
{
  int N, X;

  std::cin >> N >> X;

  std::vector<int> S(N);

  for (int i = 0; i < N; i++)
  {
    std::cin >> S[i];
  }

  std::sort(S.begin(), S.end());

  std::vector<std::vector<long long int>> dp(N, std::vector<long long int>(X + 1));

  for (int i = 0; i <= X; i++)
  {
    dp[0][i] = i % S[0];
  }

  for (int i = 1; i < N; i++)
  {
    for (int j = 0; j <= X; j++)
    {
      dp[i][j] = (1ll * dp[i - 1][j] * i + dp[i - 1][j % S[i]]) % MOD;
    }
  }

  std::cout << dp[N - 1][X] << std::endl;
}
