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;
vector<int> a, del, cou, good;
int gcd(int a, int b) {
  while (b) b ^= a ^= b ^= a %= b;
  return a;
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < (n); i++) {
    int m;
    scanf("%d", &m);
    a.push_back(m);
  }
  for (int i = 2; i * i <= k; i++) {
    if (k % i == 0) {
      del.push_back(i);
      cou.push_back(0);
      good.push_back(0);
    }
    for (; k % i == 0; k /= i) cou[cou.size() - 1]++;
  }
  if (k != 1) {
    del.push_back(k);
    cou.push_back(1);
    good.push_back(0);
  }
  for (int i = 0; i < (n); i++) {
    for (int j = 0; j < del.size(); j++) {
      if (a[i] % (int)round(pow(del[j], cou[j])) == 0) {
        good[j] = 1;
      }
    }
  }
  for (int i = 0; i < (del.size()); i++) {
    if (good[i] == 0) {
      printf("%s", "NO");
      return 0;
    }
  }
  printf("%s", "YES");
  return 0;
}