Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. GCD Table

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConsider 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*.

Input

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}).

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/20/2020 16:26:18 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|