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>
const int nmax = 1e6;
int ancient[1 + nmax];
int divv[1 + nmax];
int main(int argc, const char* argv[]) {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(0);
  std::cout.tie(0);
  int n, k, best;
  std::cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    std::cin >> ancient[i];
  }
  for (int d = 2; d * d <= k; ++d) {
    if (k % d == 0) {
      best = 1;
      while (k % d == 0) {
        best = best * d;
        k /= d;
      }
      divv[++divv[0]] = best;
    }
  }
  if (k) {
    divv[++divv[0]] = k;
  }
  for (int i = 1; i <= divv[0]; ++i) {
    int bulit(0);
    for (int j = 1; j <= n && !bulit; ++j) {
      if (ancient[j] % divv[i] == 0) {
        bulit = 1;
      }
    }
    if (!bulit) {
      std::cout << "NO";
      return 0;
    }
  }
  std::cout << "YES";
}