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 n, k, c[1000006], lpf[1000006], ok = 1;
int expo[1000006];
void fact(int x) {
  int val, p;
  while (x != 1) {
    p = 0;
    val = lpf[x];
    while (x % val == 0) {
      x /= val;
      p++;
    }
    expo[val] = max(expo[val], p);
  }
}
void factk(int x) {
  int p, val;
  while (x != 1) {
    p = 0;
    val = lpf[x];
    while (x % val == 0) {
      x /= val;
      p++;
    }
    if (p > expo[val]) ok = 0;
  }
}
int main() {
  int i, j;
  std::ios::sync_with_stdio(false);
  cin >> n >> k;
  for (i = 1; i <= n; i++) cin >> c[i];
  lpf[1] = 1;
  for (i = 2; i <= 1000000; i++)
    if (!lpf[i]) {
      lpf[i] = i;
      for (j = i * 2; j <= 1000000; j += i)
        if (lpf[j] == 0) lpf[j] = i;
    }
  for (i = 1; i <= n; i++) fact(c[i]);
  factk(k);
  if (ok)
    cout << "Yes";
  else
    cout << "No";
  return 0;
}