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_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k, a, k1;
  int p = 2;
  vector<int> pr(1000001, 0);
  pr[1] = 0;
  while (p < 1000001) {
    if (pr[p] == 0) {
      for (int i = p; i < 1000001; i += p) {
        pr[i] = p;
      }
    }
    p++;
  }
  cin >> n >> k;
  map<int, int> m;
  for (int i = 0; i < n; i++) {
    cin >> a;
    while (a > 1) {
      k1 = 0;
      p = pr[a];
      while (a % p == 0) {
        k1++;
        a /= p;
      }
      if (m.find(p) == m.end()) m[p] = 0;
      m[p] = max(m[p], k1);
    }
  }
  while (k > 1) {
    if (m[pr[k]] <= 0) {
      cout << "No";
      return 0;
    }
    m[pr[k]]--;
    k /= pr[k];
  }
  cout << "Yes";
}