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::cmp::*;
use std::collections::*;
use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: usize = read();
    let k: usize = read();

    let mut a: Vec<usize> = (0..n).map(|_| read()).collect();
    for _i in 0..min(k, 2000) {
        let mut imos: Vec<i64> = vec![0; n];
        for i in 0..n {
            let left = max(0, i as i64 - a[i] as i64);
            let right = i + a[i] + 1;
            imos[left as usize] += 1;
            if right < n {
                imos[right as usize] -= 1;
            }
            //println!("{:?}",imos);
        }
        a[0] = imos[0] as usize;
        for j in 1..n {
            imos[j] += imos[j - 1];
            a[j] = imos[j] as usize;
        }
        //println!("{:?}",imos);
    }
    let f = n - 1;
    for i in 0..n {
        if i == f{
            println!("{}",a[i]);
        }else{
            print!("{} ",a[i]);
        }
    }
}