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Sgt. Laugh

By reborn · Limits 2.5s, 256 MB

That's it. Sgt. Laugh has had enough. He is determined to end the evil military reign of General Cry. But Laugh isn't stupid. He knows, he needs a team to break through the walls of Cry.

Platoon "BattleCry'' has nn soldiers. Laugh will choose kk of these soldiers. The platoon is lined up. Height of the soldier ii is represented by hih_i. The sergeant wiil choose the soldiers in a way so that their heights form a strictly increasing sequence, i.e. if he chooses soldiers with indices i1, i2,.. ik1, iki_1, ~i_2, .. ~i_{k-1}, ~i_k where i1<i2<i3..<iki_1 < i_2 < i_3 .. < i_k , condition hi1<hi2<hi3..<hikh_{i_1} < h_{i_2} < h_{i_3} .. < h_{i_k} must hold. Also since the sergeant is a little bit picky, the height difference between the tallest and shortest soldier must be minimum possible.

Help Laugh choose the squad.

Input

First line of input contains two integers n, kn, ~k .
The following line contains nn integers representing the heights of the soldiers hih_i.

Constraints

  • 1n2×1051 \leq n \leq 2 \times 10^5 .
  • 1kmin(n, 30)1 \leq k \leq \min(n, ~30) .
  • 1hi1091 \leq h_i \leq 10^9 .

Output

If no such squad could be formed, print 1-1 on a line.

Otherwise, output the minimum possible difference between the tallest and shortest soldier in the chosen squad.

Samples

InputOutput
5 3
12 14 11 12 15
3
InputOutput
5 3
5 4 1 4 4
-1

Discussion

Statistics


39% Solution Ratio

tmwilliamlin168Earliest, Jan '20

tmwilliamlin168Fastest, 0.7s

Mr_BangladeshLightest, 12 MB

Deshi_TouristShortest, 950B

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