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>
int p[1000005], c[1000005];
using namespace std;
vector<int> vec;
int cnt[105];
int main() {
  int n, k, i, j, pcnt = 0, ind = 0, sz, tm;
  cin >> n >> k;
  for (i = 1; i <= n; i++) cin >> c[i];
  for (i = 2; i <= k; i++) {
    if (i * i > k) break;
    for (j = 1; j <= pcnt; j++) {
      if (p[j] * p[j] > i) {
        j = pcnt + 1;
        break;
      }
      if (i % p[j] == 0) break;
    }
    if (j == pcnt + 1) p[++pcnt] = i;
  }
  for (i = 1; i <= pcnt; i++) {
    if (k % p[i] == 0) {
      vec.push_back(p[i]);
      while (k % p[i] == 0) {
        k /= p[i];
        cnt[ind]++;
      }
      ind++;
    }
    if (k == 1) break;
  }
  if (k > 1) {
    vec.push_back(k);
    cnt[ind] = 1;
  }
  sz = vec.size();
  for (i = 1; i <= n; i++) {
    for (j = 0; j < sz; j++) {
      tm = cnt[j];
      while (c[i] % vec[j] == 0) {
        if (cnt[j] == 0) break;
        c[i] /= vec[j];
        cnt[j]--;
      }
      if (cnt[j] > 0) cnt[j] = tm;
    }
  }
  for (i = 0; i < sz; i++)
    if (cnt[i] > 0) break;
  if (i == sz)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
  return 0;
}