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: Runtime Error)

use std::io::*;
//use std::str::*;

fn main() {
	let s = get_in();
	let vec = s.split_whitespace().map(|num| num.parse::<usize>().unwrap()).collect::<Vec<usize>>();
	let (n, k) = (vec[0], vec[1]);
	
	let s = get_in();
	let mut vec = s.split_whitespace().map(|num| num.parse::<usize>().unwrap()).collect::<Vec<usize>>();
	for i in 0..k {
		
		let hoge = i + vec[i];
		let fuga = if i<hoge {i + 1} else {i-hoge};
		vec = vec![0; n];
		let hoge = hoge*2;
		for ii in fuga..hoge {
			vec[ii] += 1;
		}
	}
	
	println!("{}", format!("{:?}", vec).replace(", ", " ").replace("[", "").replace("]", ""))
}

fn get_in() -> String {
	let mut buf = String::new();
	stdin().read_line(&mut buf).ok();
	
	buf
}