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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in);) {
			int num = sc.nextInt();
			int k = sc.nextInt();

			int a[] = new int[num];

			for (int i = 0; i < num; i++) {
				a[i] = sc.nextInt();

			}

			for (int times = 0; times < k; times++) {
				int akarusa[] = new int[num];
				for (int i = 0; i < a.length; i++) {
					for (int j = -a[i]; j <= a[i]; j++) {
						if (0 <= i + j && i + j < akarusa.length) {
							akarusa[i + j]++;
						}

					}
				}

				boolean flag = true;
				for (int i = 0; i < a.length; i++) {
					if (a[i] != akarusa[i])
						flag = false;
				}
				if (flag) {
					break;
				} else {
					a = akarusa;
				}

			}

			for (int i = 0; i < a.length; i++) {
				System.out.print(a[i] + " ");
			}

		} catch (Exception e) {
			e.printStackTrace();
		}

	}
}