A catalog lists n prices. Consider every unordered pair of distinct list positions and the absolute difference of their two prices. There are n * (n - 1) / 2 such differences. Find the k-th smallest of these differences (counting multiplicity).
Input format
Line 1: two integers n and k.
Line 2: n space-separated integers, the prices.
Output format
A single integer: the k-th smallest absolute pairwise difference.
Constraints
- 2 <= n <= 40
- 0 <= each price <= 1000000000
- 1 <= k <= n * (n - 1) / 2