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 lp[1000000 + 5];
int cnt[1000000 + 5];
int main() {
  int i, j, v;
  int m = 1;
  for (i = 2; i <= 1000000; i++)
    if (!lp[i])
      for (j = i; j <= 1000000; j += i) lp[j] = i;
  int n, k;
  scanf("%d %d", &n, &k);
  for (i = 1; i <= n; i++) {
    scanf("%d", &v);
    while (v != 1) {
      int cp = lp[v], c = 0;
      while (v % cp == 0) {
        v /= cp;
        c++;
      }
      cnt[cp] = max(cnt[cp], c);
    }
  }
  for (i = 2; i <= 1000000; i++)
    for (j = 1; j <= cnt[i]; j++) m = ((long long int)m * i) % k;
  m = m % k;
  if (!m)
    puts("Yes");
  else
    puts("No");
  return 0;
}