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;

long long D[201][100001], MOD=1000000007;

int main()
{
    int n, x, a;
    cin >> n >> x;
    vector <int> A;
    for (int i = 0; i < n; i++)
    {
        cin >> a;
        A.push_back(a);
    }
    sort(A.begin(),A.end());
    for (int i = 0; i <= x; i++)
    {
        for (int y = 1; y <= n; y++)
        {
            D[y][i] = 0;
        }
        D[0][i] = i;
    }
    for (int i = 0; i < n; i++)
    {
        for (int y = 0; y <= x; y++)
        {
            D[i+1][y] += D[i][y] * i;
            D[i+1][y] %= MOD;
            D[i+1][y] += D[i][y % A[i]];
            D[i+1][y] %= MOD;
        }
    }
    cout << D[n][x];
    return 0;
}
