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 <map>
#include <vector>
#include <algorithm>

using namespace std;

int main() {
    long long MOD = 1000000007LL;
    int n, x;
    cin >> n >> x;
    vector <int> s;
    for (int i = 0; i < n; i++) {
        int t;
        cin >> t;
        s.push_back(t);
    }
    sort(s.begin(), s.end());

    vector <long long> m1(x + 1);
    m1[x] = 1;
    for (int i = n - 1; i >= 0; i--) {
        vector <long long> m2(x + 1);
        for (int m = 0; m <= x; m++) {
            long long t = m1[m];
            int v = m % s[i];
            m2[v] = (m2[v] + t) % MOD;
            m2[m] = (m2[m] + t * i) % MOD;
        }
        m1 = m2;
    }
    long long ret = 0;
    for (int m = 0; m <= x; m++) {
        long long t = m1[m];
        ret = (ret + m * t) % MOD;
    }
    cout << ret << endl;
    return 0;
}
