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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use competitive::prelude::*;

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

    // for n in 1..1000 {
    //     let mut a = vec![0; n];

    //     for i in 0..n {
    //         if a.iter().all(|r| *r == n) {
    //             eprintln!("{}: {}", n, i + 1);
    //             break;
    //         }

    //         let mut na = vec![0; n];

    //         for i in 0..n {
    //             let mut t = 0;

    //             for j in 0..n {
    //                 if a[j] >= (i as i64 - j as i64).abs() as usize {
    //                     t += 1;
    //                 }
    //             }

    //             na[i] = t;
    //         }

    //         a = na;
    //     }
    // }

    for _ in 0..k {
        if a.iter().all(|r| *r == n) {
            break;
        }

        let mut delta = vec![0 as i64; n + 1];

        for i in 0..n {
            let l = max(0, i as i64 - a[i] as i64) as usize;
            let r = min(n - 1, i + a[i]);
            delta[l] += 1;
            delta[r + 1] -= 1;
        }

        let mut cur = 0 as i64;

        for i in 0..n {
            cur += delta[i];
            a[i] = cur as usize;
        }
    }

    echo!(a);
}
*/

fn main() {
    let exe = "/tmp/bin0CC8438A";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";