cf 687B Remainders Game （剩余定理）

B. 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 c₁, c₂, ..., 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 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.

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.

      题意：给了k和n个数ci，并且如果需要的话可以认为x%ci是已知的，判断任意一个满足条件的x%k是否是确定的。

     思路：根据剩余定理，如果我们想知道x%m等于多少，当且仅当我们知道x%m1,x%m2..x%mr分别等于多少，其m1*m2...*mr=m，并且mi相互互质，即构成独立剩余系。令m的素数分解为m=p1^k1*p2^k2...*pr^kr，如果任意i，都有pi^ki的倍数出现在集合中，那么m就能被猜出来。
        这个问题等价于问LCM(ci)%m是否等于0。

         一开始也不会做的，只是感觉和crt有关，数论学得太渣了，后来看贴吧里卿学姐贴出来的讨论贴写的。http://tieba.baidu.com/p/4641314203。今天来做下笔记，总结一下。

详细见代码：

#include
#include
#include
#include
#include
#include
using namespace std;
const int maxn = 1e5+100;
typedef long long LL;
LL gcd(LL a,LL b) { return b==0 ? a:gcd(b,a%b);}
LL lcm(LL a,LL b){ return a/gcd(a,b)*b; }
int main()
{
	int n,k,a,i;
	scanf("%d%d",&n,&k);
	LL ans=1;
	for(i=1;i<=n;i++)
	{
		scanf("%d",&a);
		ans=lcm(ans,a)%k;
	}
	printf("%s\n",ans==0 ? "Yes":"No");
	return 0;
}