D. Building Bombing
time limit per test
3 seconds
memory limit per test
1024 mebibytes
input
standard input
output
standard output

KAIST has a series of $$$N$$$ buildings in a row, numbered from $$$1$$$ to $$$N$$$, from left to right. Building $$$i$$$ has a height of $$$h_i$$$. Building $$$i$$$ is visible from the left if and only if every building on its left has a height strictly less than $$$h_i$$$.

Your lab is located in building number $$$L$$$. Since your favorite number is $$$K$$$, you want to make your lab building the $$$K$$$-th tallest building visible from the left. To achieve your goal, you will blow up some of the buildings.

For example, suppose there are $$$N=7$$$ buildings in a row and their heights are $$$[10, 30, 90, 40, 60, 60, 80]$$$. Your lab is located at building number $$$L=2$$$ and your favorite number is $$$K=3$$$. After blowing up buildings $$$3$$$ and $$$7$$$, the buildings visible from the left will be buildings $$$1$$$, $$$2$$$, $$$4$$$, and $$$5$$$. Then your lab becomes the $$$3$$$rd tallest building visible from the left, as desired.

What is the minimum number of buildings to blow up to make your lab building the $$$K$$$-th tallest building visible from the left?

Input

The first line contains three space-separated integers $$$N$$$, $$$L$$$, and $$$K$$$.

The second line contains $$$N$$$ space-separated integers $$$h_1, \dots, h_N$$$.

  • $$$1 \le L \le N \le 100\,000$$$
  • $$$1 \le K \le 10$$$
  • $$$1 \le h_i \le 10^9$$$ ($$$1 \le i \le N$$$)
Output

Output the minimum number of buildings to blow up to make your lab building the $$$K$$$-th tallest building visible from the left. If it is impossible to do so, output $$$-1$$$ instead.

Examples
Input
7 2 3
10 30 90 40 60 60 80
Output
2
Input
3 2 2
30 20 10
Output
-1