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 inf = (int)1e9;
const int mod = 1e9 + 7;
using namespace std;
int n, k;
int c[1000011];
int p[1000011], cntp[1000011], col[1000011];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  int maxc = k;
  for (int i = 1; i <= n; i++) {
    cin >> c[i];
    maxc = max(maxc, c[i]);
  }
  for (int i = 2; i <= maxc; i++) {
    if (!p[i]) {
      for (int j = i; j <= maxc; j += i) {
        p[j] = i;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    while (c[i] > 1) {
      int cnt = 0;
      int x = p[c[i]];
      while (p[c[i]] == x) {
        cnt++;
        c[i] /= p[c[i]];
      }
      cntp[x] = max(cntp[x], cnt);
    }
  }
  bool ans = 1;
  while (k > 1) {
    col[p[k]]++;
    if (col[p[k]] > cntp[p[k]]) {
      ans = 0;
    }
    k /= p[k];
  }
  if (ans) {
    cout << "Yes";
  } else
    cout << "No";
  return 0;
}