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 N = 1e6 + 100;
int f[N];
map<int, int> m;
int k;
int n;
int arr[N];
void in(int t) {
  int v = t;
  while (t != 1) {
    int x = f[t];
    int cnt = 0;
    while (t % x == 0) {
      t /= x, cnt++;
    }
    if (v != k) {
      if (m.count(x) > 0)
        if (cnt >= m[x]) m[x] = 0;
    } else if (v == k) {
      m[x] = cnt;
    }
  }
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  memset(f, -1, sizeof(f));
  f[0] = f[1] = 1;
  for (int i = 2; i <= N - 100; i++) {
    for (int j = 1; i * j <= N - 100; j++) {
      if (f[i * j] == -1) f[i * j] = i;
    }
  }
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i];
  }
  in(k);
  for (int i = 1; i <= n; i++) {
    if (arr[i] == k) {
      cout << "YES";
      return 0;
    } else
      in(arr[i]);
  }
  for (map<int, int>::iterator it = m.begin(); it != m.end(); it++) {
    if (it->second != 0) {
      cout << "NO";
      return 0;
    }
  }
  cout << "YES";
}