Problem3355--GCD Table

3355: GCD Table

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

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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