Range Minimum Queries

You are given an integer sequence A of length N and an integer K. You will perform the following operation on this sequence Q times:

• Choose a contiguous subsequence of length K, then remove the smallest element among the K elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like).

Let X and Y be the values of the largest and smallest element removed in the Q operations. You would like X-Y to be as small as possible. Find the smallest possible value of X-Y when the Q operations are performed optimally.

Constraints

• 1 \leq N \leq 2000
• 1 \leq K \leq N
• 1 \leq Q \leq N-K+1
• 1 \leq A_i \leq 10^9
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K Q A_1 A_2 ... A_N

Output

Print the smallest possible value of X-Y.

Examples

Input

5 3 2 4 3 1 5 2

Output

1

Input

10 1 6 1 1 2 3 5 8 13 21 34 55

Output

7

Input

11 7 5 24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784

Output

451211184

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N K Q A_1 A_2 ... A_N

outputFormat

Output

Print the smallest possible value of X-Y.

Examples

Input

5 3 2 4 3 1 5 2

Output

1

Input

10 1 6 1 1 2 3 5 8 13 21 34 55

Output

7

Input

11 7 5 24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784

Output

451211184

样例

11 7 5
24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784

451211184