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#5804

Aggressive Cows 1s 256MB

Problems

Farmer John has built a new long barn, with N (2 <= N <= 100,000) stalls. The stalls are located along a straight line at positions x1,...,xN (0 <= xi <= 1,000,000,000).

His C (2 <= C <= N) cows don't like this barn layout and become aggressive towards each other once put into a stall. To prevent the cows from hurting each other, FJ want to assign the cows to the stalls, such that the minimum distance between any two of them is as large as possible. What is the largest minimum distance?


Input

Line 1: Two space-separated integers: N and C

Lines 2..N+1: Line i+1 contains an integer stall location, xi


Output

Line 1: One integer: the largest minimum distance


Example

5 3
1
2
8
4
9
3

FJ can put his 3 cows in the stalls at positions 1, 4 and 8, resulting in a minimum distance of 3.



Source

USACO 2005 February Gold 2번. Aggressive cows

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