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(void) {
  int i, j, n, k;
  scanf("%d%d", &n, &k);
  vector<int> kp;
  for (i = 2; i * i <= k; i++)
    if (k % i == 0) {
      int x = 1;
      while (k % i == 0) {
        k /= i;
        x *= i;
      }
      kp.push_back(x);
    }
  if (k > 1) kp.push_back(k);
  for (i = 0; i <= (int)(n)-1; i++) {
    int c;
    scanf("%d", &c);
    for (j = 0; j <= (int)(kp.size()) - 1; j++) {
      if (c % kp[j] == 0) kp.erase(kp.begin() + j--);
    }
  }
  if (kp.size() == 0)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}