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 <vector>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;

#define MOD 1000000007
#define REP(i, N) for (int i = 0; i < N; ++i)
#define REP1(i, N) for (int i = 1; i <= N; ++i)
#define RREP(i, N) for (int i = N - 1; i >= 0; --i)
#define ALL(a) a.begin(), a.end()

ll dp[201][100001];

int main() {
  int n, x;
  cin >> n >> x;
  vector<int> s(n);
  REP(i, n) cin >> s[i];
  sort(ALL(s));
  for (int i = 0; i <= x; ++i) dp[0][i] = i;
  REP(i, n) for (int j = 0; j <= x; ++j) {
    dp[i + 1][j] += dp[i][j % s[i]];
    dp[i + 1][j] %= MOD;
    dp[i + 1][j] += (i * dp[i][j]) % MOD;
    dp[i + 1][j] %= MOD;
  }
  cout << dp[n][x] << endl;
  return 0;
}