Codeforces Round #360 (Div. 2) D. Remainders Game(中国剩余定理)

原题链接

D. Remainders Game

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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, ..., cn 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, ..., 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 52 3 5 12

output

Yes

input

2 72 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.

根据中国剩余定理可以求出x%lcm(c1,c2..cn)的值，若lcm(c1,c2..cn)是k的倍数，则x%k的值也能确定

#include <iostream>#include <cstdio>#include <algorithm>#include <cstring>#define INF 1e9using namespace std;typedef long long ll;ll gcd(ll a, ll b){return b ? gcd(b, a % b) : a;}int main(){ll n, k, a, lcm = 1;scanf("%I64d%I64d", &n, &k);while(n--){scanf("%I64d", &a);lcm = lcm / gcd(lcm, a) * a % k;}    if(lcm % k == 0)     puts("Yes");    else     puts("No");return 0;}