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 f[1111111];
int to[1111111];
int allc[1111111];
int cc[1111111];
vector<int> wasc;
void fillcc(int x) {
  if (x < 2) {
    return;
  }
  const int fx = f[x];
  if (cc[fx] == 0) {
    wasc.push_back(fx);
  }
  cc[fx]++;
  fillcc(to[x]);
}
int main() {
  f[1] = 1;
  for (int i = 2; i < 1111111; i++) {
    if (f[i] == 0) {
      f[i] = i;
      for (int j = i + i; j < 1111111; j += i) {
        if (f[j] == 0) {
          f[j] = i;
          to[j] = j / i;
        }
      }
    }
  }
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    fillcc(x);
    for (int c : wasc) {
      allc[c] = max(allc[c], cc[c]);
      cc[c] = 0;
    }
    wasc.clear();
  }
  fillcc(k);
  for (int i : wasc) {
    if (cc[i] > allc[i]) {
      cout << "No";
      return 0;
    }
  }
  cout << "Yes";
  return 0;
}