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 <algorithm>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <sstream>
#include <string>
#include <vector>
using namespace std;
typedef long long ll;
const ll MOD = 1000000007;

int main(int argc, const char * argv[]) {
  
  ll N, X; cin >> N >> X;
  vector<ll> S(N);
  for (int i=0; i<N; i++)
    cin >> S[i];
  
  sort(S.begin(), S.end(), greater<ll>());
  
  vector<vector<ll>> dp(N+1, vector<ll>(X+1, 0));
  dp[0][X] = 1;
  for (ll n=0; n<N; n++) {
    for (ll x=0; x<X+1; x++) {
      if (dp[n][x] == 0) continue;
      dp[n+1][x%S[n]] += dp[n][x];
      dp[n+1][x%S[n]] %= MOD;
      dp[n+1][x] += (N-n-1)*dp[n][x]%MOD;
      dp[n+1][x] %= MOD;
    }
  }
  
  ll ans = 0;
  for (int i=0; i<X+1; i++){
    ans += dp[N][i]*i % MOD;
    ans %= MOD;
  }
  cout << ans << endl;
  
  return 0;
}
