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::collections::BinaryHeap;
// use std::cmp::Reverse;
use itertools::Itertools;

fn main() {
    input! {
        n: usize,
        k: usize,
        a: [i64; n],
    }

    let mut now = a;
    for _ in 0..k {
        if now.iter().all(|x| *x == n as i64) {
            break;
        }

        let mut diff = vec![0i64; n];
        for i in 0..n {
            if now[i] as usize <= i {
                diff[i - now[i] as usize] += 1;
            } else {
                diff[0] += 1;
            }
            if i + (now[i] as usize + 1) < n {
                diff[i + now[i] as usize + 1] -= 1;
            }
        }

        // dbg!(&diff);

        let mut next = vec![0; n];
        let mut nv = 0;
        for i in 0..n {
            nv += diff[i];
            next[i] = nv;
        }

        now = next;
    }

    let ans = now.iter().join(" ");
    println!("{}", ans);
}