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 proconio::input;
use std::cmp::{min, max};

fn main() {
    input! {
        n : usize,
        k : usize,
        a : [i64; n]
    };
    let mut end = k;
    let mut res = vec![vec![0; n]; 2];
    let mut add : Vec<i64> = vec![0; n+1];
    for i in 0..n { res[0][i] = a[i]; }
    for i in 0..k {
        for j in 0..=n { add[j] = 0 }
        for j in 0..n {
            add[max(0, j as i64 - res[i%2][j]) as usize] += 1;
            add[min(n as i64, j as i64 + 1 + res[i%2][j]) as usize] -= 1;
        }
        res[1-i%2][0] = add[0];
        for j in 1..n {
            res[1-i%2][j] = res[1-i%2][j-1] + add[j];
        }
        let mut ok = true;
        for j in 0..n {
            if res[1-i%2][j] != n as i64 { ok = false; }
        }
        if ok {
            end = i+1;
            break;
        }
    }
    for i in 0..n { print!("{} ", res[end%2][i]) }
    println!("");
}