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;
long long gcd(long long a, long long b) { return a == 0 ? b : gcd(b % a, a); }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
int main() {
  long long n, k;
  long long a, ans;
  int flag = 0;
  while (~scanf("%lld%lld", &n, &k)) {
    ans = 1;
    for (int i = 1; i <= n; i++) {
      scanf("%lld", &a);
      ans = lcm(ans, a);
      ans = gcd(ans, k);
      if (ans == k) {
        flag = 1;
      }
    }
    if (flag == 1)
      printf("YES");
    else
      printf("NO");
  }
}