Remainders Game
题意翻译
给定正整数 $n,k$ 和 $n$ 个正整数 $c_1,c_2,\cdots,c_n$。如果对于任意正整数 $x$,可以通过 $x\mod c_i$ 的值推出 $x\mod k$ 的值则输出 `Yes` 否则输出 `No`。
题目描述
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 ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF687B/74cc0e497602c391113efb814a12e06ebc180bd8.png). There are $ n $ ancient numbers $ c_{1},c_{2},...,c_{n} $ and Pari has to tell Arya ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF687B/d6826eab3568be14654e0e163000c670f1c64e14.png) 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 ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF687B/74cc0e497602c391113efb814a12e06ebc180bd8.png) for any positive integer $ x $ ?
Note, that ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF687B/cb1d84ad58154eb7ea26b65d1ae0039570db9bb6.png) means the remainder of $ x $ after dividing it by $ y $ .
输入输出格式
输入格式
The first line of the input contains two integers $ n $ and $ k $ ( $ 1<=n,\ k<=1000000 $ ) — the number of ancient integers and value $ k $ that is chosen by Pari.
The second line contains $ n $ integers $ c_{1},c_{2},...,c_{n} $ ( $ 1<=c_{i}<=1000000 $ ).
输出格式
Print "Yes" (without quotes) if Arya has a winning strategy independent of value of $ x $ , or "No" (without quotes) otherwise.
输入输出样例
输入样例 #1
4 5
2 3 5 12
输出样例 #1
Yes
输入样例 #2
2 7
2 3
输出样例 #2
No
说明
In the first sample, Arya can understand ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF687B/b93dce9b9ef400fa12cce1ab52784e3449739731.png) because $ 5 $ is one of the ancient numbers.
In the second sample, Arya can't be sure what ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF687B/34daaca50b46751e5d9e1271dc07f186fd9fd248.png) 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 $ .