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

D. 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, ..., 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 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.

#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <map>
#include <iostream>
using namespace std;
#define ll long long
ll lcm;
const int maxn = 1e6 + 10;
ll getlcm(ll a, ll b) {
    return a / __gcd(a, b) * b;
}

ll p[maxn];

int main() {
    ll n, k;
    while(~scanf("%I64d %I64d", &n, &k)) {
        for(int i = 1; i <= n; i++) scanf("%I64d", &p[i]);
        ll lcm = 1;
        int flag = 0;
        for(int i = 1; i <= n; i++) {
            lcm = getlcm(lcm, p[i]);
            lcm = lcm % k;
            if(lcm == 0) {
                puts("Yes");
                flag = 1;
                break;
            }
        }
        if(!flag) puts("No");
    }
}