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.*;

public class Main{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int n = Integer.parseInt(scan.next());
		int k = Integer.parseInt(scan.next());
		int[] a = new int[n];
		for(int i = 0;i < n; ++i){
			a[i] = Integer.parseInt(scan.next());
		}
		int[] isumo = new int[n];
		for(int i = 0;i < k; ++i){
			for(int j = 0;j < n; ++j){
				int start = Math.max(j-a[j],0);
				int end = j+a[j]+1;
				isumo[start]++;
				if(end < n){
					isumo[end]--;
				}

				}
				a[0] = isumo[0];
				isumo[0] = 0;
				for(int j = 1;j < n ; ++j){
					a[j] = a[j-1]+isumo[j];
					isumo[j] = 0;
				}
		}
		for(int i = 0;i < n; ++i){
			System.out.print(a[i]+" ");
		}


	}
}