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 prime[1000005], lcm[1000005];
int N = 1000000;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  for (int i = (int)(2); i <= (int)(N); i++)
    if (!prime[i]) {
      for (int j = i; j <= N; j += i) prime[j] = i;
    }
  for (int i = (int)(1); i <= (int)(n); i++) {
    int x;
    cin >> x;
    while (x > 1) {
      int p = prime[x], count = 0;
      while (x % p == 0) {
        x /= p;
        count++;
      }
      lcm[p] = max(lcm[p], count);
    }
  }
  while (k > 1) {
    int p = prime[k], count = 0;
    while (k % p == 0) {
      k /= p;
      count++;
    }
    if (count > lcm[p]) {
      cout << "No";
      return 0;
    }
  }
  cout << "Yes";
}