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>
#define rep(i, a, n) for(int i = a; i < n; i++)
#define int long long
using namespace std;
typedef pair<int, int> P;
const int mod = 1000000007;
const int INF = 1e18;

int dp[210][100010];

signed main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int n, x;
    cin >> n >> x;
    vector<int> s(n);
    rep(i, 0, n){
        cin >> s[i];
    }
    sort(s.rbegin(), s.rend());
    dp[0][x] = 1;
    rep(i, 0, n){
        rep(j, 0, 100001){
            if(dp[i][j] == 0) continue;
            (dp[i + 1][j % s[i]] += dp[i][j]) %= mod;
            (dp[i + 1][j] += dp[i][j] * (n - 1 - i) % mod) %= mod;
        }
    }
    int ans = 0;
    rep(i, 0, 100001){
        (ans += i * dp[n][i] % mod) %= mod;
    }
    cout << ans << endl;
}