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: Time Limit Exceeded)

use std::cmp::min;
use std::io::stdin;

fn main() {
    let mut is = String::new();
    stdin().read_line(&mut is).ok();
    let mut itr = is.split_whitespace().map(|e| e.parse::<usize>().unwrap());
    let n: usize = itr.next().unwrap();
    let k: usize = itr.next().unwrap();
    is.clear();
    stdin().read_line(&mut is).ok();
    let mut a = is
        .split_whitespace()
        .map(|e| e.parse::<usize>().unwrap())
        .collect::<Vec<usize>>();

    for _ in 0..k {
        let mut b = vec![0usize; n + 1];
        for i in 0..n {
            let l = i.saturating_sub(a[i]);
            let r = min(i + a[i] + 1, n);
            b[l] = b[l].wrapping_add(1);
            b[r] = b[r].wrapping_add(!0);
        }
        a = vec![0; n];
        for i in 0..n {
            a[i] = a[if i > 0 { i - 1 } else { 0 }].wrapping_add(b[i]);
        }

        if a.iter().all(|e| e == &0) {
            break;
        }
    }

    let mut flg = false;
    for e in a {
        if flg {
            print!(" ");
        }
        print!("{}", e);
        flg = true;
    }
    println!();
}