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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

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

    int numOfLamps = sc.nextInt();
    int numOfReps = sc.nextInt();

    int[] brightnessArray = new int[numOfLamps];
    for(int i = 0; i < brightnessArray.length; i++){
      brightnessArray[i] = sc.nextInt();
    }

    //continue k times
    for(int n = 0; n < numOfReps; n++){

      int[] sumArray = new int[numOfLamps];

      int[] leftArray = new int[numOfLamps];
      int[] rightArray = new int[numOfLamps];
      for(int i = 0; i < brightnessArray.length; i++){
        for(int j = 0; j < numOfLamps; j++){
          if( j <= ( i + brightnessArray[i] + 0.5 ) && j >= ( i - brightnessArray[i] - 0.5 ) ){
            sumArray[j]++;
          }
        }
      }

      //if final print out final sums
      if( n == (numOfReps - 1) ){
        for( int i = 0; i < sumArray.length; i++ ){
          System.out.print(sumArray[i]+" ");
        }
      }

      //change values
      for(int i = 0; i < brightnessArray.length; i++){
        brightnessArray[i] = sumArray[i];
      }






      /*
      //go through lamps
      for(int i = 0; i < brightnessArray.length; i++){
        int sum = 0;
        //check neighbors if radius includes current position
        for(int j = 0; j < brightnessArray.length; j++){
          if( i <= ( j + brightnessArray[j] + 0.5 ) && i >= ( j - brightnessArray[j] - 0.5 ) ){
            sum++;
          }
        }
        //store sum values
        sumArray[i] = sum;
      }

      //change values
      for(int i = 0; i < brightnessArray.length; i++){
        brightnessArray[i] = sumArray[i];
      }

      //if final print out final sums
      if( n == (numOfReps - 1) ){
        for( int i = 0; i < sumArray.length; i++ ){
          System.out.print(sumArray[i]+" ");
        }
      }

      */
    }

  }
}