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 n, k, m, a[30], b[30], c;
bool flag[30];
int main() {
  memset(a, 0, sizeof(a));
  memset(b, 0, sizeof(b));
  scanf("%d%d", &n, &k);
  m = 0;
  for (int i = 2; i <= k; i++)
    if (k % i == 0) {
      a[m] = i;
      while (k % i == 0) {
        k /= i;
        b[m]++;
      }
      m++;
    }
  memset(flag, 0, sizeof(flag));
  for (int i = 0; i < n; i++) {
    scanf("%d", &c);
    for (int j = 0; j < m; j++)
      if (!flag[j] && c % a[j] == 0) {
        int cnt = 0;
        while (c % a[j] == 0) {
          cnt++;
          c /= a[j];
        }
        if (cnt >= b[j]) flag[j] = 1;
      }
  }
  for (int i = 0; i < m; i++)
    if (!flag[i]) {
      printf("No\n");
      return 0;
    }
  printf("Yes\n");
  return 0;
}