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B. Chat

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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.

Input

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*.

Output

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.

Examples

Input

6 0

0 1 1 2 3 2

Output

1 2 2 3 3 3

Input

10 1

0 1 0 3 4 5 2 3 7 0

Output

2 3 3 4 5 6 6 6 8 2

Input

2 2

0 1

Output

2 2

Note

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.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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