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.Comparator;
import java.util.Scanner;

public class Main {

    long MOD = (long)1e9 + 7;

    void run() {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int X = sc.nextInt();

        Integer[] a = new Integer[n];
        for (int i = 0; i < n; i++) a[i] = sc.nextInt();
        Arrays.sort(a, Comparator.reverseOrder());
        long[][] dp = new long[2][X + 1];
        dp[0][X] = 1;
        int sw = 0;
        for (int i = 0; i < n; i++) {
            sw = 1 - sw;
            Arrays.fill(dp[sw], 0);
            for (int x = 0; x <= X; x++) if (dp[1 - sw][x] > 0) {
                dp[sw][x % a[i]] = (dp[sw][x % a[i]] + dp[1 - sw][x]) % MOD;
                dp[sw][x] = (dp[sw][x] + dp[1 - sw][x] * (n - i - 1)) % MOD;
            }
//            debug(dp[sw]);
        }

        long sum = 0;
        for (int x = 0; x <= X; x++) {
            sum += dp[sw][x] * x;
            sum %= MOD;
        }
        System.out.println(sum);
    }

    void debug(Object...os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}
