Problem: Today Pari and Arya are playing a game called Remainders.

Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?

Note, that <image> means the remainder of x after dividing it by y.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 1 000 000) — the number of ancient integers and value k that is chosen by Pari.

The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 1 000 000).

Output

Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.

Examples

Input

4 5
2 3 5 12


Output

Yes


Input

2 7
2 3


Output

No

Note

In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.

In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, k, tmp;
  set<int> c;
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> tmp;
    c.insert(tmp);
  }
  vector<int> f;
  for (int i = 2; i * i <= k; i++) {
    if (k % i == 0) {
      int t = 1;
      while (k % i == 0) {
        t *= i;
        k /= i;
      }
      f.push_back(t);
    }
  }
  if (k > 1) f.push_back(k);
  bool check;
  string res = "YES";
  for (int i = 0; i < f.size(); i++) {
    check = false;
    for (auto ci : c) {
      if (ci % f[i] == 0) {
        check = true;
        break;
      }
    }
    if (!check) {
      res = "NO";
      break;
    }
  }
  cout << res;
}