Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

5 3 2
4 3 1 5 2

Sample Output 1

1

In the first operation, whichever contiguous subsequence of length 3 we choose, the minimum element in it is 1.
Thus, the first operation removes A_3=1 and now we have A=(4,3,5,2).
In the second operation, it is optimal to choose (A_2,A_3,A_4)=(3,5,2) as the contiguous subsequence of length 3 and remove A_4=2.
In this case, the largest element removed is 2, and the smallest is 1, so their difference is 2-1=1.

Sample Input 2

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

Sample Output 2

7

Sample Input 3

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

Sample Output 3

451211184

Solution in LuaJIT (2.0.4) (judge verdict: Accepted)

local mfl, mce = math.floor, math.ceil
local mmi, mma = math.min, math.max
local bls, brs = bit.lshift, bit.rshift

local n, k, q = io.read("*n", "*n", "*n")
local a = {}
local b = {}
local used = {}
for i = 1, n do
  a[i] = io.read("*n")
  b[i] = i
  used[i] = false
end
table.sort(b, function(x, y) return a[x] < a[y] end)

local ret = a[b[q]] - a[b[1]]
for i = 1, n do
  local topidx = b[i]
  used[topidx] = true
  local tmp = {}
  local cand = {}
  for j = 1, n do
    if used[j] then
      table.sort(tmp)
      for z = 1, #tmp - k + 1 do
        table.insert(cand, tmp[z])
      end
      tmp = {}
    else
      table.insert(tmp, a[j])
    end
  end
  table.sort(tmp)
  for z = 1, #tmp - k + 1 do
    table.insert(cand, tmp[z])
  end
  if #cand < q then break end
  table.sort(cand)
  ret = mmi(ret, cand[q] - cand[1])
end
print(ret)