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: Runtime Error)

import java.io.*;
import java.util.Scanner;
import java.util.Arrays;
import java.util.ArrayList;
import java.math.BigDecimal;

public class Main{

    public static void main(String[] args){
        //START

        Scanner sc=new Scanner(System.in);

        int N=sc.nextInt();
        int K=sc.nextInt();

        int[] A=new int[20000];
        int[] B=new int[20000];

        int c=0;
		int NN=N+10000;
      
        int in=0;
        for(in=10000;in<NN;in++){
            A[in]=sc.nextInt();
            B[in]=0;
        }

        int g=0;
        int h=0;
        int i=0;
        int j=0;

        for(g=0;g<K;g++){
            for(h=10000;h<NN;h++){
                for(i=h-A[h];i<=h+A[h];i++){
                    B[i]++;
                }

                if(h==NN-1){
                  for(j=10000;j<NN;j++){
                    A[j]=B[j];
                    B[j]=0;
                  }
                }
            }
        }  
        for(in=10000;in<NN;in++){
            System.out.print(A[in]+"\t");
        }

        //END
    }
}