404457: GYM101510 C Computer Science

Vera has N integers a₁, ..., a_N. A margin is a non-negative integer L such that it is possible to choose N integers x₁, ..., x_N such that for all i, 1 ≤ i ≤ N, the interval [x_i, x_i + L] contains at least K of Vera's integers and also contains a_i.

Compute the minimum possible margin.

Line 1 contains integers N and K (1 ≤ K ≤ N ≤ 2 × 10⁵).

Line 2 contains N integers, a₁, ..., a_N ( - 10⁹ ≤ a_i ≤ 10⁹).

Print one line with one integer, the minimum possible margin.

5 3
1 -2 10 5 4

6

For the first example, one possible solution is to choose x₁ =  - 1, x₂ =  - 2, x₃ = 4, x₄ = 0, x₅ = 0, which is illustrated below.