Remainders Game

1000ms

262144K

Description:

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 $\text{[math]}$ . There are n ancient numbers c₁, c₂, ..., c_n and Pari has to tell Arya $\text{[math]}$ 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 $\text{[math]}$ for any positive integer x?

Note, that $\text{[math]}$ 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, ..., 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.

Sample Input:

4 5
2 3 5 12

Sample Output:

Yes

Sample Input:

2 7
2 3

Sample Output:

No

Note:

In the first sample, Arya can understand $\text{[math]}$ because 5 is one of the ancient numbers.

In the second sample, Arya can't be sure what $\text{[math]}$ 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.

Informação

Provedor Codeforces

Código CF687B