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 k, n;
vector<int> v, u;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr), cout.tie(nullptr);
  cin >> n >> k;
  for (int i = 2; i * i <= k; i++) {
    if (k % i == 0) v.push_back(i), u.push_back(0);
    while (k % i == 0) {
      k /= i;
      u.back()++;
    }
  }
  if (k > 1) v.push_back(k), u.push_back(1);
  for (int i = 0; i < n; i++) {
    int c;
    cin >> c;
    for (int j = 0; j < v.size(); j++)
      if (~v[j]) {
        int tmp = 0;
        while (c % v[j] == 0) {
          tmp++;
          c /= v[j];
        }
        if (tmp >= u[j]) v[j] = -1;
      }
  }
  for (auto i : v)
    if (~i) return cout << "No\n", 0;
  cout << "Yes\n";
  return 0;
}