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 gcd(int a, int b) {
  while (b) {
    a %= b;
    if (!a) return b;
    b %= a;
  }
  return a;
}
int main(void) {
  int k, n, tmp;
  long long int res = 0;
  scanf("%d %d", &n, &k);
  short answer = 0;
  while (n--) {
    scanf("%d", &tmp);
    tmp = gcd(tmp, k);
    if (!res)
      res = tmp;
    else {
      res = (res * tmp) / gcd(res, tmp);
    }
    if (!(res % k)) {
      answer = 42;
    }
  }
  if (answer)
    printf("Yes\n");
  else
    printf("No\n");
  return 0;
}