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 FOR(i,k,n)  for(int i = (k);i < (n);++i)
#define REP(i,n)    FOR(i,0,n)
#define ALL(x)      begin(x),end(x)

using namespace std;
using vecint = vector<int>;
using ll = int64_t;

constexpr ll MOD = 1000000007;

int main()
{
  ll n,x;
  cin>>n>>x;
  vector<ll> s(n);
  REP(i,n) cin>>s[i];
  sort(ALL(s));
  vector<ll> dp(x+1);
  dp[x] = 1;
  REP(i,n) {
    vector<ll> tmp(x+1);
    REP(j,x+1) {
      if (dp[j] == 0) continue;
      int cnt = 0;
      REP(k,n) {
        if (s[k] > j) ++cnt;
        else {
          ll next = j%s[k];
          tmp[next] += dp[j];
          tmp[next] %= MOD;
        }
      }
      tmp[j] += dp[j] * (cnt - i);
      tmp[j] %= MOD;
    }
    swap(dp, tmp);
  }
  ll ans = 0;
  REP(i,x+1) {
    ans += i * dp[i];
    ans %= MOD;
  }
  cout << ans << endl;
  return 0;
}
