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 mod = 1e9 + 7;
struct ele {
  int x, c, re;
};
std::vector<ele> QQ;
int main() {
  int n, m, t, y, p, k, i;
  scanf("%d%d", &n, &m);
  for (k = 2; k <= m; k++) {
    if (m % k == 0) {
      t = 0;
      while (m % k == 0) {
        t++;
        m /= k;
      }
      QQ.push_back(ele{k, t, 0});
    }
  }
  for (k = 1; k <= n; k++) {
    scanf("%d", &y);
    for (i = 0; i < QQ.size(); i++) {
      p = QQ[i].x;
      t = 0;
      while (y % p == 0) {
        t++;
        y /= p;
      }
      if (t > QQ[i].re) QQ[i].re = t;
    }
  }
  int in = 1;
  for (k = 0; k < QQ.size(); k++) {
    if (QQ[k].re < QQ[k].c) in = 0;
  }
  if (in) {
    puts("Yes");
  } else {
    puts("No");
  }
}