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
import java.util.Arrays;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    long M = 1_000_000_007;
    int N = scanner.nextInt();
    int X = scanner.nextInt();
    int[] a = new int[N];
    for (int i = 0; i < N; i++) a[i] = scanner.nextInt();
    Arrays.sort(a);

    long[][] dp = new long[N + 1][X + 1];
    for (int i = 0; i <= X; i++) dp[0][i] = i;
    for (int i = 1; i <= N; i++) {
      for (int j = 0; j <= X; j++) {
        dp[i][j] = (long)(i - 1) * dp[i - 1][j] % M;
        dp[i][j] += dp[i - 1][j % a[i - 1]];
        dp[i][j] %= M;
      }
    }
    System.out.println(dp[N][X]);
  }
}
