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>
const long long MAXN = int(1e6);
using namespace std;
long long st[MAXN], k[MAXN], f[MAXN];
int main() {
  long long n, m, kol = 0, i, j;
  scanf("%I64d%I64d\n", &n, &m);
  for (i = 2; i <= sqrt(m); i++)
    while (m % i == 0) {
      m /= i;
      if (st[kol] == i)
        k[kol] *= i;
      else
        st[++kol] = i, k[kol] = i;
    }
  if (m > 1) k[++kol] = m;
  for (i = 1; i <= n; i++) {
    long long a;
    scanf("%I64d", &a);
    for (j = 1; j <= kol; j++)
      if (a % k[j] == 0) f[j] = 1;
  }
  for (i = 1; i <= kol; i++)
    if (f[i] != 1) {
      cout << "No" << endl;
      return 0;
    }
  cout << "Yes" << endl;
  return 0;
}