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 proconio::*;

fn run() {
    input! {
        n: usize,
        k: usize,
        mut a: [usize; n],
    }
    for _ in 0..k {
        let mut imos = vec![0; n + 1];
        for (i, &a) in a.iter().enumerate() {
            let l = if a > i {
                0
            } else {
                i - a
            };
            let r = if i + a + 1 > n {
                n
            } else {
                i + a + 1
            };
            imos[l] += 1;
            imos[r] -= 1;
        }
        for i in 1..=n {
            imos[i] += imos[i - 1];
        }
        let mut fill = true;
        for (a, &imos) in a.iter_mut().zip(imos.iter()) {
            *a = imos;
            fill &= imos == n;
        }
        if fill {
            break;
        }
    }
    let mut s = String::new();
    for a in a {
        s.push_str(&format!("{} ", a));
    }
    s.pop();
    println!("{}", s);
}

fn main() {
    run();
}