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 main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  long long k;
  cin >> n >> k;
  vector<long long> c(n);
  for (int i = 0; i < n; i++) {
    cin >> c[i];
  }
  vector<long long> f;
  for (int i = 2; i * i <= k; i++) {
    if (k % i == 0) {
      f.push_back(1);
      while (k % i == 0) {
        f.back() *= i;
        k /= i;
      }
    }
  }
  if (k != 1) {
    f.push_back(k);
  }
  bool ok = true;
  for (long long x : f) {
    bool ok2 = false;
    for (int i = 0; i < n; i++) {
      if (c[i] % x == 0) {
        ok2 = true;
      }
    }
    if (!ok2) {
      ok = false;
    }
  }
  if (ok) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
}