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 max_n = 11111111, inf = 1111111111;
int n, k, res[max_n];
int mn[max_n];
int main() {
  mn[1] = 1;
  for (int i = 2; i < max_n; ++i) {
    if (mn[i] == 0) {
      mn[i] = i;
      for (int j = 2 * i; j < max_n; j += i) {
        if (mn[j] == 0) {
          mn[j] = i;
        }
      }
    }
  }
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; ++i) {
    int x;
    scanf("%d", &x);
    while (x > 1) {
      int cnt = 0, q = mn[x];
      while (x % q == 0) {
        x /= q;
        ++cnt;
      }
      res[q] = max(res[q], cnt);
    }
  }
  while (k > 1) {
    int cnt = 0, q = mn[k];
    while (k % q == 0) {
      k /= q;
      ++cnt;
    }
    if (cnt > res[q]) {
      printf("No\n");
      return 0;
    }
  }
  printf("Yes\n");
  return 0;
}