p03343 AtCoder Regular Contest 098 - 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
```python
N, K, Q = map(int, input().split())
X = list(map(int, input().split()))

r = 10**18
for y in X:
    tmp = []
    tmp2 = []
    for x in X:
        if x < y:
            tmp.sort()
            tn = len(tmp)
            if len(tmp) > K-1:
                tmp2 += tmp[:tn-K+1]
            tmp = []
            continue
        tmp.append(x)
    tmp.sort()
    tn = len(tmp)
    if tn-K+1 > 0:
        tmp2 += tmp[:tn-K+1]
    tmp2.sort()
    if len(tmp2) >= Q:
        r = min(r, tmp2[Q-1] - y)
print(r)

```