A train has $n$ cabins arranged in a line. Some cabins are occupied by passengers, and some are empty. You are given an array $cabins$ of length $n$ where:

• $cabins_i = 1$ if cabin $i$ has a passenger,
• $cabins_i = 0$ if it is empty.

Passengers can switch places with passengers in adjacent cabins in one move.

For example, in $[1, 0, 0, 1, 0, 1]$ with $k = 2$, moving the 4^th passenger one step to the right gives two consecutive passengers in 1 move.

Your task is to compute the minimum number of moves required so that $k$ passengers end up sitting in $k$ consecutive cabins.

The first line contains two integers $n$ and $k$ ($1 \leq k \leq n \leq 10^5$) — the number of cabins and the number of passengers to be grouped together.

The second line contains $n$ integers $cabins_1, cabins_2, \dots, cabins_n$ ($cabins_i \in \lbrace 0, 1 \rbrace$) — the occupancy state of each cabin.

It is guaranteed that the array contains at least $k$ passengers in total.

Print the minimum number of moves required so that there exists a group of $k$ passengers sitting together in $k$ consecutive cabins.