Building Blocks

Byteasar has arranged blocks into $n$ columns. The $i$-th column has height $h_i$, meaning it is made of $h_i$ blocks.

He picks an integer $k$ and wants to make some $k$ consecutive columns all have the same height. He may only use the following two kinds of moves:

• place one block on top of any column (there is always an unlimited supply of spare blocks), or
• remove the topmost block from any column.

Each move adds or removes exactly one block and counts as one move. Find the minimum number of moves needed so that some $k$ consecutive columns all have equal height.

The first line contains two integers $n$ and $k$ separated by a single space ($1 \le k \le n \le 100\,000$).

Each of the next $n$ lines contains one integer: the $i$-th of them is $h_i$, the height of the $i$-th column ($0 \le h_i \le 1\,000\,000$).

Print a single integer: the minimum number of moves needed so that some $k$ consecutive columns all have equal height.