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>
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(0);
  int n, k;
  std::cin >> n >> k;
  if (k == 1) {
    std::cout << "Yes\n";
    return 0;
  }
  std::vector<int> A(n);
  std::vector<std::pair<int, int> > need;
  int cur = 2;
  while (k > 1) {
    int cnt = 0;
    while (k % cur == 0) {
      k /= cur;
      cnt++;
    }
    if (cnt) need.push_back(std::make_pair(cur, cnt));
    cur++;
  }
  std::vector<bool> done(((int)(need).size()));
  for (int i = 0; i < (n); ++i) {
    std::cin >> A[i];
    int ind = 0;
    for (auto& pr : (need)) {
      int cnt = 0;
      while (A[i] % pr.first == 0) cnt++, A[i] /= pr.first;
      if (cnt >= pr.second) done[ind] = true;
      ind++;
    }
  }
  for (int i = 0; i < (((int)(done).size())); ++i)
    if (done[i] == false) {
      std::cout << "No\n";
      return 0;
    }
  std::cout << "Yes\n";
  return 0;
}