You are given N integers a = {a_i}. Let b = {b_j} be such K numbers (not necessarily integers), that:
and S — minimal.
Find S.
First line contains two numbers N and K. Second line contains exactly N integers — {a_i}.
Only real number S with absolute or relative error not greater than 10^{-8}.
Limits
1 ≤ N ≤ 5000
1 ≤ K ≤ N
0 ≤ a_i ≤ 400000