Maximizing Condensation in Chapters

You are given a sequence of n positive integers a₁, a₂, ..., a_n which represent the "conceptual values" of materials. You need to partition the sequence exactly into k contiguous and non-empty segments (chapters). For the i-th segment which covers indices [l_i, r_i], define its chapter value b_i as the maximum element in that segment, i.e.,

\( b_i = \max_{j \in [l_i, r_i]} \{a_j\} \)

Then, the condensation of the entire composition is defined as the greatest common divisor (GCD) of these chapter values:

\( \gcd(b_1, b_2, \ldots, b_k) \)

Your task is to determine the maximum possible condensation that can be obtained by partitioning the sequence into exactly k segments optimally.

inputFormat

The first line contains two integers n and k (1 ≤ k ≤ n), representing the number of materials and the number of chapters respectively.

The second line contains n positive integers a₁, a₂, ..., a_n, where a_i represents the conceptual value of the i-th material.

outputFormat

Output a single integer — the maximum possible condensation (i.e. the maximum value of \( \gcd(b_1, b_2, \ldots, b_k) \) ) that can be achieved by an optimal partition.

sample

5 2
4 6 8 2 10

4