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;
const int maxn = 5e5;
int a[maxn], b[maxn], c[maxn];
int n, K, i, j, x, y, bl, la;
int main() {
  scanf("%d%d", &n, &K);
  x = K;
  for (i = 2; i <= x; i++)
    if (x % i == 0) {
      a[++la] = i;
      while (x % i == 0) {
        b[la]++;
        x /= i;
      }
    }
  for (i = 1; i <= n; i++) {
    scanf("%d", &x);
    for (j = 1; j <= la; j++) {
      y = 0;
      while (x % a[j] == 0) {
        y++;
        x /= a[j];
      }
      c[j] = max(c[j], y);
    }
  }
  bl = 1;
  for (i = 1; i <= la; i++)
    if (c[i] < b[i]) {
      bl = 0;
      break;
    }
  if (bl)
    printf("Yes");
  else
    printf("No");
  return 0;
}