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;
const int MAXN = 1e6 + 5;
int cnt[MAXN] = {0}, prime[MAXN] = {0};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int n, k;
  cin >> n >> k;
  for (int i = 2; i < MAXN; i++) {
    if (!prime[i]) {
      for (int j = i; j < MAXN; j += i) {
        prime[j] = i;
      }
    }
  }
  int x;
  for (int i = 0; i < n; i++) {
    cin >> x;
    while (x > 1) {
      int c = 0;
      int p = prime[x];
      while (x % p == 0) {
        c++;
        x /= p;
      }
      cnt[p] = max(cnt[p], c);
    }
  }
  int ok = 1;
  while (k > 1) {
    ok &= (cnt[prime[k]] > 0);
    cnt[prime[k]]--;
    k /= prime[k];
  }
  if (ok)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}