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 n, k;
int c;
std::vector<std::pair<int, int> > factor;
bool know[50];
int main() {
  scanf("%d%d", &n, &k);
  for (int d = 2, x; d * d <= k; d++)
    if (k % d == 0) {
      for (x = 0; k % d == 0;) {
        k /= d;
        x++;
      }
      factor.push_back(std::make_pair(d, x));
    }
  if (k > 1) factor.push_back(std::make_pair(k, 1));
  for (; n > 0; n--) {
    scanf("%d", &c);
    for (int i = 0, x; i < factor.size(); i++)
      if (c % factor[i].first == 0) {
        for (x = 0; c % factor[i].first == 0;) {
          c /= factor[i].first;
          x++;
        }
        if (x >= factor[i].second) know[i] = true;
      }
  }
  bool can_know = true;
  for (int i = 0; i < factor.size(); i++) can_know = can_know & know[i];
  printf(can_know ? "Yes\n" : "No\n");
  return 0;
}