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;
void zanj0() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
unordered_map<int, int> cnt;
const int N = 1e6 + 5;
int seive[N];
void pre() {
  for (int i = 1; i < N; i++) seive[i] = i;
  for (int i = 2; i * i < N; i++) {
    if (seive[i] == i) {
      for (int j = i * i; j < N; j += i) {
        seive[j] = i;
      }
    }
  }
}
void getFact(int num) {
  unordered_map<int, int> temp;
  while (num > 1) {
    int div = seive[num];
    temp[div]++;
    num /= div;
  }
  for (auto& it : temp) {
    cnt[it.first] = max(cnt[it.first], it.second);
  }
}
void solve() {
  pre();
  int n, k;
  cin >> n >> k;
  int x;
  for (int i = 0; i < n; i++) {
    cin >> x;
    getFact(x);
  }
  for (auto& it : cnt) {
    while (k > 1 && k % it.first == 0 && it.second) {
      it.second--;
      k /= it.first;
    }
  }
  cout << (k == 1 ? "YES" : "NO") << "\n";
}
int32_t main() {
  zanj0();
  solve();
  cerr << "Time : " << 1000 * (long double)clock() / (long double)CLOCKS_PER_SEC
       << "ms\n";
  return 0;
}