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;

const int Mod = 1e9 + 7;
#define N 406
#define M 200005

int n, a[N], X;
long long f[N][M];

inline bool cmp(int x, int y) { return x > y;}

int main() {
    cin >> n >> X;
    for (int i = 1; i <= n; ++i)
        scanf("%d", a + i);
    sort(a + 1, a + n + 1, cmp);
    f[0][X] = 1;
    for (int i = 1; i <= n; ++i)
        for (int j = 0; j <= 1e5; ++j)
            (f[i][j % a[i]] += f[i - 1][j]) %= Mod,
            (f[i][j] += f[i - 1][j] * (n - i) % Mod) %= Mod;
    long long ans = 0;
    for (int i = 0; i <= 1e5; ++i)
        (ans += f[n][i] * i % Mod) %= Mod;
    cout << ans << endl;
    return 0;
}
