# GCD Table

## 题目描述

Consider a table $G$ of size $n×m$ such that $G(i,j)=GCD(i,j)$ for all $1<=i<=n,1<=j<=m$ . $GCD(a,b)$ is the greatest common divisor of numbers $a$ and $b$ . You have a sequence of positive integer numbers $a_{1},a_{2},...,a_{k}$ . We say that this sequence occurs in table $G$ if it coincides with consecutive elements in some row, starting from some position. More formally, such numbers $1<=i<=n$ and $1<=j<=m-k+1$ should exist that $G(i,j+l-1)=a_{l}$ for all $1<=l<=k$ . Determine if the sequence $a$ occurs in table $G$ .

## 输入输出格式

### 输入格式

The first line contains three space-separated integers $n$ , $m$ and $k$ ( $1<=n,m<=10^{12}$ ; $1<=k<=10000$ ). The second line contains $k$ space-separated integers $a_{1},a_{2},...,a_{k}$ ( $1<=a_{i}<=10^{12}$ ).

### 输出格式

Print a single word "YES", if the given sequence occurs in table $G$ , otherwise print "NO".

## 输入输出样例

### 输入样例 #1

100 100 5
5 2 1 2 1


### 输出样例 #1

YES


### 输入样例 #2

100 8 5
5 2 1 2 1


### 输出样例 #2

NO


### 输入样例 #3

100 100 7
1 2 3 4 5 6 7


### 输出样例 #3

NO


## 说明

Sample 1. The tenth row of table $G$ starts from sequence {1, 2, 1, 2, 5, 2, 1, 2, 1, 10}. As you can see, elements from fifth to ninth coincide with sequence $a$ . Sample 2. This time the width of table $G$ equals 8. Sequence $a$ doesn't occur there.