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: Time Limit Exceeded)

use proconio::input;

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

	let mut b = a;

	let mut k = k;
	if k > 41 {
		k = 41;
	}
	for _i in 0..k {
		let mut sum: Vec<usize> = vec![0; n];
		for j in 0..n {
			let start;
			if b[j] > j {
				start = 0;
			}
			else {
				start = j - b[j];
			}
			let mut end = j + b[j] + 1;
			if end > n {
				end = n
			}
			for p in start..end {
				sum[p] += 1;
			}
		}
		b = sum;
	}
	for i in 0..n-1 {
		print!("{} ", b[i]);
	}
	println!("{}", b[n-1]);
}