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 <iomanip>
#include <string>
#include <vector>
#include <algorithm>
#define REP(i,n) for(int i=0;i<(n);++i)
using namespace std;
typedef long long int LL;
typedef vector<LL> VL;
#define SMAX 100001
#define MOD 1000000007

int main() {
  LL N, X;
  cin >> N >> X;
  VL S;
  REP(i, N) {
    int s;
    cin >> s;
    S.push_back(s);
  }
  sort(S.begin(), S.end(), greater<LL>());
  
  LL C[SMAX] = {};
  C[X] = 1;
  REP(i, N) {
    int tS = S[i];
    LL nC[SMAX] = {};
    REP(j, SMAX) {
      nC[j%tS] += C[j];
      nC[j] += C[j] * (N - i - 1);
    }
    REP(j, SMAX) {
      C[j] = nC[j] % MOD;
    }
  }
  LL sum = 0;
  REP(i, SMAX) {
    sum += C[i] * i;
    sum %= MOD;
  }
  cout << sum << endl;
}