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5983: GCD Table

内存限制：256 MB 时间限制：2 S
题面：传统 评测方式：文本比较 上传者：
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题目描述

D. GCD Table
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
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 a1,a2,...,ak. 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)=al for all 1≤l≤k.
Determine if the sequence a occurs in table G.
Input
The first line contains three space-separated integers n, m and k (1≤n,m≤1012; 1≤k≤10000). The second line contains k space-separated integers a1,a2,...,ak (1≤ai≤1012).
Output
Print a single word "YES", if the given sequence occurs in table G, otherwise print "NO".
Examples
Input 
100 100 5
5 2 1 2 1
Output 
YES
Input 
100 8 5
5 2 1 2 1
Output 
NO
Input 
100 100 7
1 2 3 4 5 6 7
Output 
NO
Note
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.

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