Winter Is Coming

Description:

Input:

The first line contains two positive integers n and k (1 ≤ n ≤ 2·10⁵, 0 ≤ k ≤ n) — the number of winter days and the number of days winter tires can be used. It is allowed to drive on winter tires at any temperature, but no more than k days in total.

The second line contains a sequence of n integers t₁, t₂, ..., t_n ( - 20 ≤ t_i ≤ 20) — the average air temperature in the i-th winter day.

Output:

Print the minimum number of times Vasya has to change summer tires to winter tires and vice versa to drive safely during all winter. If it is impossible, print -1.

Sample Input:

4 3
-5 20 -3 0

Sample Output:

2

Sample Input:

4 2
-5 20 -3 0

Sample Output:

4

Sample Input:

10 6
2 -5 1 3 0 0 -4 -3 1 0

Sample Output:

3

Note:

In the first example before the first winter day Vasya should change summer tires to winter tires, use it for three days, and then change winter tires to summer tires because he can drive safely with the winter tires for just three days. Thus, the total number of tires' changes equals two.

In the second example before the first winter day Vasya should change summer tires to winter tires, and then after the first winter day change winter tires to summer tires. After the second day it is necessary to change summer tires to winter tires again, and after the third day it is necessary to change winter tires to summer tires. Thus, the total number of tires' changes equals four.