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A10384. Remainders Game

编程题 普及/提高-

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 ![](/uploads/acgo/image/b9c8ca92781c9a00_9c0c61dec34c.jpeg). There are $n$ ancient numbers $c_{1},c_{2},...,c_{n}$ and Pari has to tell Arya ![](/uploads/luogu/CF687B/d6826eab3568be14654e0e163000c670f1c64e14_a77497c177c8.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 ![](/uploads/acgo/image/b9c8ca92781c9a00_9c0c61dec34c.jpeg) for any positive integer $x$ ?

Note, that ![](/uploads/acgo/image/1aa426dcd855e9e8_988c29ed959c.jpeg) means the remainder of $x$ after dividing it by $y$ .

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 #1
4 5
2 3 5 12
输出 #1
Yes
输入 #2
2 7
2 3
输出 #2
No

说明/提示

In the first sample, Arya can understand ![](/uploads/acgo/image/6308585e7d5cd259_eb38774e10ee.jpeg) because $5$ is one of the ancient numbers.

In the second sample, Arya can't be sure what ![](/uploads/acgo/image/48d31bb8487e4c05_11adf923b0c3.jpeg) is. For example $1$ and $7$ have the same remainders after dividing by $2$ and $3$ , but they differ in remainders after dividing by $7$ .
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