Problem Statement

We have an integer sequence of length $N$: $A=(A_1,A_2,\cdots,A_N)$. Below in this problem, let the score of $A$ be the sum of the first $K$ terms of $A$. Additionally, let $s$ be the score of the sequence $A$ given in input.

You can do the following operation any number of times.

• Choose two adjacent elements of $A$ and swap them.

Your objective is to make the score at least $s+1$. Determine whether the objective is achievable. If it is, find the minimum number of operations needed to achieve it.

Constraints

• $2 \leq N \leq 4 \times 10^5$
• $1 \leq K \leq N-1$
• $1 \leq A_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

If the objective is not achievable, print -1. If it is achievable, print the minimum number of operations needed to achieve it.