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 <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <random>
#include <bitset>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
using namespace std;
const ll MOD = 1000000007LL;

ll dp[205][100005];
// i番目まで見て、あまりがjである時の場合の数

int main() {
    int n, x;
    cin >> n >> x;

    int s[n];
    for (int i = 0; i < n; i++) cin >> s[i];

    sort(s, s+n, greater<int>());

    dp[0][x] = 1;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j <= x; j++) {
            (dp[i+1][j] += dp[i][j] * (n - i - 1)) %= MOD;
            (dp[i+1][j%s[i]] += dp[i][j]) %= MOD;
        }
    }

    ll ans = 0LL;
    for (int j = 1; j < s[n-1]; j++) {
        (ans += dp[n][j] * j) %= MOD;
    }

    cout << ans << "\n";
    return 0;
}