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::{BufRead, Write};
use std::cmp;

fn main() {
    let stdin = std::io::stdin();
    let stdout = std::io::stdout();
    let mut reader = std::io::BufReader::new(stdin.lock());
    let mut writer = std::io::BufWriter::new(stdout.lock());

    let (n, k): (usize, usize) = {
        let mut buf = String::new();
        reader.read_line(&mut buf).unwrap();
        let mut iter = buf.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    };

    let mut a: Vec<i32> = {
        let mut buf = String::new();
        reader.read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        iter.map(|x| x.parse().unwrap()).collect()
    };

    for _ in 0..k {
        let mut b: Vec<i32> = vec![0; n as usize];
        let m = n as i32;
        for i in 0..n {
            let x = i as i32;
            let left = cmp::max(0, x - a[i]) as usize;
            let right = cmp::min(m - 1, x + a[i]) as usize;
            b[left] += 1;
            if right + 1 < n as usize {
                b[right + 1] -= 1;
            }
        }

        let mut flag = b[0] == m as i32;
        for i in 1..n {
            b[i] += b[i - 1];
            if b[i] < m {
                flag = false;
            }
        }

        a = b;
        if flag { break; }
    }

    let a = a.iter().map(|x| x.to_string()).collect::<Vec<_>>().join(" ");
    writeln!(writer, "{}", a).unwrap();
}