As a teaser for the final exam, Farhan gives a small array and asks: among all increasing subsequences of a given length K, what's the largest possible GCD? Read an array of N integers and an integer K. Among all increasing subsequences of length exactly K, print the MAXIMUM possible GCD of the subsequence's elements, or -1 if no increasing subsequence of length K exists. (Hint: for each candidate divisor d from large to small, keep only elements divisible by d, and check if an increasing subsequence of length ≥K exists among them — this is a direct simplified version of the hardest problem from your real contest set.)
Input
Line1: N K. Line2: N integers.
Output
Maximum GCD, or -1.
Constraints
1 ≤ K ≤ N ≤ 500, 1 ≤ a_i ≤ 500
Sample Input
5 3 4 8 6 12 3
Sample Output
4
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