Codeforces Round # (Div. 2) D. Remainders Game (Chinese remainder theorem)

D. remainders Game

Today Pari and Arya are playing a game called remainders.

Pari chooses, positive integer  x  and  K , and tells Arya  k  but not  x . Arya has to find the value . There Are  n  ancient numbers  c Span class= "Lower-index" >1, C 2, ..., c N  and Pari have to tell Arya  if Arya wants. Given  K  and The ancient values, tell us if Arya have a winning strategy Independe NT of value Of  x  or not. Formally, is it true this Arya can understand the value  for any positive integer  x ?

Note, that's means the remainder of x after dividing it by y.

Input

The first line of the input contains the integers n and k (1≤ n, K ≤1 -the number of ancient integers and value k that's chosen by Pari.

The second line contains n integers c1, C2, ..., c n (1≤ ci ≤1).

Output

Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (Witho UT quotes) otherwise.

Examplesinput

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. For example 1 and 7 has the same remainders after dividing by 2 and 3, but they differ in remainders afte R dividing by 7.

#include <cstdio>#include<cmath>#include<cstring>#include<algorithm>#include<map>#include<iostream>using namespacestd;#definell Long Longll LCM;Const intMAXN = 1e6 +Ten; ll GETLCM (ll A, ll b) {returnA/__GCD (A, b) *b;} ll P[MAXN];intMain () {ll n, K;  while(~SCANF ("%i64d%i64d", &n, &k)) { for(inti =1; I <= N; i++) scanf ("%i64d", &P[i]); ll LCM=1; intFlag =0;  for(inti =1; I <= N; i++) {LCM=GETLCM (LCM, p[i]); LCM= LCM%K; if(LCM = =0) {puts ("Yes"); Flag=1;  Break; }        } if(!flag) puts ("No"); }}

Codeforces Round #(Div. 2) D. Remainders Game (Chinese remainder theorem)