Problem:
Score : 500 points

Problem Statement

We have N bulbs arranged on a number line, numbered 1 to N from left to right.
Bulb i is at coordinate i.

Each bulb has a non-negative integer parameter called intensity.
When there is a bulb of intensity d at coordinate x, the bulb illuminates the segment from coordinate x-d-0.5 to x+d+0.5.
Initially, the intensity of Bulb i is A_i. We will now do the following operation K times in a row:

For each integer i between 1 and N (inclusive), let B_i be the number of bulbs illuminating coordinate i. Then, change the intensity of each bulb i to B_i.

Find the intensity of each bulb after the K operations.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq K \leq 2 \times 10^5

0 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \ldots A_N

Output

Print the intensity A{'}_i of each bulb i after the K operations to Standard Output in the following format:

A{'}_1 A{'}_2 \ldots A{'}_N

Sample Input 1

5 1
1 0 0 1 0

Sample Output 1

1 2 2 1 2

Initially, only Bulb 1 illuminates coordinate 1, so the intensity of Bulb 1 becomes 1 after the operation.
Similarly, the bulbs initially illuminating coordinate 2 are Bulb 1 and 2, so the intensity of Bulb 2 becomes 2.

Sample Input 2

5 2
1 0 0 1 0

Sample Output 2

3 3 4 4 3

Solution in Rust (1.42.0) (judge verdict: Accepted)

use std::io;
use std::str::FromStr;
use std::cmp::*;
use std::collections::BinaryHeap;

fn input_tuple() -> (i64, i64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<i64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn input_vec() -> Vec<i64> {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.split_whitespace().map(|s| s.parse().unwrap()).collect()
}

fn main() {
    let (n, k) = input_tuple();
    let mut a_vec = input_vec();

    if k * n > 100_000_000 {
        for _ in 0..n {
            print!("{} ", n);
        }
        println!();
        return;
    }
    // let mut a_vec = vec![0; n as usize];
    for _ in 0..k {
        let mut queue: BinaryHeap<i64> = BinaryHeap::new();
        let mut count = 0;
        let mut next = vec![1; n as usize];
        for j in 0..n {
            // println!("j = {}", j);
            // println!("{:?}", queue);
            while !queue.is_empty() {
                if j == -queue.peek().unwrap() {
                    count -= 1;
                    queue.pop();
                } else {
                    break;
                }
            }
            next[j as usize] += count;
            // println!("{}", j+a_vec[j as usize]+1);
            queue.push(-(j+a_vec[j as usize]+1));
            count += 1;
        }

        let mut queue: BinaryHeap<i64> = BinaryHeap::new();
        let mut count = 0;
        for j in (0..n).rev() {
            while !queue.is_empty() {
                if j == *queue.peek().unwrap() {
                    count -= 1;
                    queue.pop();
                } else {
                    break;
                }
            }
            next[j as usize] += count;
            // println!("{}", j-a_vec[j as usize]-1);
            queue.push(j-a_vec[j as usize]-1);
            count += 1;
        }
        a_vec = next;
    }
    for a in a_vec {
        print!("{} ", a);
    }
    println!();
}