codeforces 360 D - Remainders Game

D - Remainders Game

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 . There are n ancient numbersc₁,

 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.

Sample Input

Input

4 52 3 5 12

Output

Yes

Input

2 72 3

Output

No

题意：给定n，k,和n个ci。你可以知道x%ci,问是否能确定x%k.分析：根据中国剩余定理问题就相当于要确定 C 数组整体的最小公倍数 lcm(c) 是否是 K 的倍数，如果是，则能确定输出 yes，否则输出 no.

#include <iostream>
#include<cstdio>
#define LL long long
using namespace std;
int a;
int gcd(LL a,LL b)
{
    return b?gcd(b,a%b):a;
}
int main()
{
    LL n,k,lcm=1;
   scanf("%lld%lld", &n, &k);
     for(int i=0;i<n;i++)
     {
           scanf("%lld", &a);
          lcm = lcm / gcd(lcm, a) * a % k;
    }
    if(lcm%k==0)  printf("Yes\n");
    else      printf("No\n");
    return 0;
}