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;
bool p[1000010];
vector<vector<int> > primhatvanyok;
int szam;
vector<int> primfelbontas;
vector<bool> kesze;
int maxom = 1000000;
int n, k;
bool lehet = true;
int main() {
  for (int i = 2; i <= maxom; i++) {
    if (p[i] == false) {
      primhatvanyok.push_back(vector<int>());
      szam++;
      int j = 2 * i;
      while (j <= maxom) {
        p[j] = true;
        j += i;
      }
      j = i;
      while (j <= maxom) {
        primhatvanyok[szam - 1].push_back(j);
        j *= i;
      }
    }
  }
  scanf("%d", &n);
  scanf("%d", &k);
  for (int i = 0; i < primhatvanyok.size(); i++) {
    if (k % primhatvanyok[i][0] == 0) {
      int tart = 0;
      while (tart < primhatvanyok[i].size() &&
             (k % primhatvanyok[i][tart] == 0))
        tart++;
      primfelbontas.push_back(primhatvanyok[i][tart - 1]);
      kesze.push_back(false);
    }
  }
  for (int i = 1; i <= n; i++) {
    int a;
    scanf("%d", &a);
    for (int i = 0; i < primfelbontas.size(); i++) {
      if (a % primfelbontas[i] == 0) kesze[i] = true;
    }
  }
  for (int i = 0; i < kesze.size(); i++) {
    if (kesze[i] == false) lehet = false;
  }
  if (lehet == false)
    cout << "No";
  else
    cout << "Yes";
}