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 itertools::Itertools as _;
use itertools_num::ItertoolsNum as _;
use proconio::input;
use std::cmp;

fn main() {
    input! {
        n: usize,
        k: usize,
        mut r#as: [usize; n],
    }

    for _ in 0..k {
        let mut imos = vec![0; n + 1];

        for (i, &a) in r#as.iter().enumerate() {
            let l = i.saturating_sub(a);
            let r = cmp::min(i + a + 1, n);
            imos[l] += 1;
            imos[r] -= 1;
        }

        r#as = imos[..n].iter().map(|&c| c as usize).cumsum().collect();

        if r#as.iter().all(|&a| a == n) {
            break;
        }
    }

    println!("{}", r#as.into_iter().format(" "));
}