GCD Table

1000ms

262144K

Description:

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, ..., 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 ≤ 10¹²; 1 ≤ k ≤ 10000). The second line contains k space-separated integers a₁, a₂, ..., a_k (1 ≤ a_i ≤ 10¹²).

Output:

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

Sample Input:

100 100 5
5 2 1 2 1

Sample Output:

YES

Sample Input:

100 8 5
5 2 1 2 1

Sample Output:

NO

Sample Input:

100 100 7
1 2 3 4 5 6 7

Sample 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.

Informação

Provedor Codeforces

Código CF338D