Remainders Game

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 . There are n ancient numbers c ₁, c ₂, …, c _n and Pari has to tell Arya  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  for any positive integer x?

Note, that  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 c ₁, c ₂, …, c _n (1 ≤ c _i ≤ 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  because 5 is one of the ancient numbers.

In the second sample, Arya can’t be sure what  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:

#include <bits/stdc++.h>

using namespace std;

inline int gcd(int a, int b) {
while (a > 0 && b > 0) {
if (a > b) {
a %= b;
} else {
b %= a;
}
}
return a + b;
}

inline int lcm(int a, int b) {
return a / gcd(a, b) * b;
}

int main() {
int n, k;
scanf("%d %d", &n, &k);
int l = 1;
for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    int g = gcd(x, k);
    l = lcm(l, g);
  }
  puts(l == k ? "Yes" : "No");
  return 0;
}