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: Wrong Answer)

import java.util.*;

public class Main{
	public static void main(String[] args){
    	Scanner sc = new Scanner(System.in);
      	int n = sc.nextInt();
      	int k = sc.nextInt();
      	int[] list = new int[n];
      	for(int cnt = 0;cnt < list.length;cnt++){
        	list[cnt] = sc.nextInt();
        }
      	for(int cnt = 0;cnt < k;cnt++){
        	swap(list);
        }
      	for(int num : list){
        	System.out.print(num + " ");
        }
    }
  	public static void swap(int[] list){
    	int save = 0;
      	int count = 1;
      	int cnt = 1;
      	for(int i = 0;i < list.length;i++){
        	for(int j = 0;j < list.length;j++){
            	if(count > (double)(cnt - list[j] - 0.5) && count < (double)(cnt + list[j] + 0.5)){
                	save++;
                }
              	cnt++;
            }
          	list[i] = save;
          	count++;
          	save = 0;
        }
    }
}