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 n, k, f[1000001], kt[1000001], cnt[1000001];
int main() {
  ios_base::sync_with_stdio(false);
  ;
  f[0] = f[1] = 1;
  for (int i = (2); i <= (1000000); i++)
    if (f[i] == 0)
      for (int j = 1; i * j <= 1000000; j++) f[i * j] = i;
  cin >> n >> k;
  while (k != 1) {
    int x = f[k], cntt = 0;
    while (k % x == 0) k /= x, cntt++;
    cnt[x] = cntt;
  }
  for (int i = (1); i <= (n); i++) {
    int res;
    cin >> res;
    while (res != 1) {
      int x = f[res], cntt = 0;
      while (res % x == 0) res /= x, ++cntt;
      if (cnt[x] > 0 && cntt >= cnt[x]) kt[x] = 1;
    }
  }
  for (int i = (1); i <= (1000000); i++)
    if (cnt[i] > 0 && kt[i] == 0) {
      cout << "No";
      return 0;
    }
  cout << "Yes" << endl;
}