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)

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

fn main() {
    struct A;
    impl Monoid for A {
        type Item = (usize, usize);
        fn identity() -> Self::Item { (0, 1) }
        fn merge(l: &Self::Item, r: &Self::Item) -> Self::Item { (l.0 + r.0, l.1 + r.1) }
    }
    struct E;
    impl Monoid for E {
        type Item = usize;
        fn identity() -> Self::Item { 0 }
        fn merge(l: &Self::Item, r: &Self::Item) -> Self::Item { l + r }
    }
    impl Effector for E {
        type Target = A;
        fn effect(t: &(usize, usize), e: &usize) -> (usize, usize) { (t.0 + e * t.1, t.1) }
    }

    input! {
        n: usize, k: usize,
        a: [usize; n]
    }
    let mut a = LazySegTree::<E>::from_slice(&a.iter().map(|&a| (a, 1)).collect_vec());
    for _ in 0..k.min(41) {
        let mut b = LazySegTree::new(n);
        for i in 0..n {
            let a = a.get(i).0;
            b.effect(i.saturating_sub(a)..(i + a + 1).min(n), &1);
        }
        a = b;
    }
    println!("{}", (0..n).map(|i| a.get(i).0.to_string()).join(" "))
}
*/

fn main() {
    let exe = "/tmp/bin4903B4E7";
    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>";