CF928B.Chat

There are times you recall a good old friend and everything you've come through together. Luckily there are social networks — they store all your message history making it easy to know what you argued over 10 years ago.

More formal, your message history is a sequence of messages ordered by time sent numbered from $1$ to $n$ where $n$ is the total number of messages in the chat.

Each message might contain a link to an earlier message which it is a reply to. When opening a message $x$ or getting a link to it, the dialogue is shown in such a way that $k$ previous messages, message $x$ and $k$ next messages are visible (with respect to message $x$ ). In case there are less than $k$ messages somewhere, they are yet all shown.

Digging deep into your message history, you always read all visible messages and then go by the link in the current message $x$ (if there is one) and continue reading in the same manner.

Determine the number of messages you'll read if your start from message number $t$ for all $t$ from $1$ to $n$ . Calculate these numbers independently. If you start with message $x$ , the initial configuration is $x$ itself, $k$ previous and $k$ next messages. Messages read multiple times are considered as one.

The first line contains two integers $n$ and $k$ ( $1<=n<=10^{5}$ , $0<=k<=n$ ) — the total amount of messages and the number of previous and next messages visible.

The second line features a sequence of integers $a_{1},a_{2},...,a_{n}$ ( 0<=a_{i}<i ), where $a_{i}$ denotes the $i$ -th message link destination or zero, if there's no link from $i$ . All messages are listed in chronological order. It's guaranteed that the link from message $x$ goes to message with number strictly less than $x$ .

Print $n$ integers with $i$ -th denoting the number of distinct messages you can read starting from message $i$ and traversing the links while possible.

Consider $i=6$ in sample case one. You will read message $6$ , then $2$ , then $1$ and then there will be no link to go.

In the second sample case $i=6$ gives you messages $5,6,7$ since $k=1$ , then $4,5,6$ , then $2,3,4$ and then the link sequence breaks. The number of distinct messages here is equal to $6$ .