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)

#![allow(non_snake_case)]
#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;
use whiteread::parse_line;
use std::collections::*;
use num::*;

use itertools::Itertools;
use itertools_num::ItertoolsNum;

#[fastout]
fn main() {
    input!{
        n: usize,
        k: usize,
        mut a_vec: [isize; n],
    }
    let mut ans_vec;
    for _ in 0..k {
        ans_vec = vec![0; n+1];
        for i in 0..n {
            let tmp = a_vec[i];
            let start = if i as isize - tmp <= 0 {
                0
            } else {
                i as isize - tmp
            };
            let end = if (n - i) as isize - tmp <= 0 {
                n as isize
            } else {
                i as isize + tmp + 1
            };
            // dbg!(&start, &end);
            ans_vec[start as usize] += 1;
            ans_vec[end as usize] -= 1;
            // dbg!(&ans_vec);
        }
        a_vec = ans_vec.iter().cumsum().collect::<Vec<isize>>()[..n].to_vec();
        if a_vec.iter().all(|&x| x == n as isize) { break; }
    }



    for a in a_vec.iter() {
        println!("{}", a);
    }
}