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) {
                Scanner scan = new Scanner(System.in);

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

                int[] A = new int[N];
                int[] temp;

                for (int i = 0; i < N; i++) {
                	A[i] = scan.nextInt();
                }

                scan.close();
                
                int count = 0;
                int tempN = N;
                
                while (tempN == 1) {
                	tempN /= 2;
                	count++;
                }

                if (K >= tempN + 10) {

                	for (int k = 0; k < N; k++) {
                    	System.out.print(N + " ");
                    }

                    System.out.println();

                } else {

	                for (int j = 0; j < K; j++) {

	                	 temp = new int[N];

	                	for (int n = 0; n < N; n++) {

	                		temp[n]++;

	                		for (int a = 1; a <= A[n]; a++) {
	                			if (n+1 + a <= N) {
	                				temp[n + a]++;
	                			}
	                			if (n+1 - a >= 1) {
	                				temp[n - a]++;
	                			}

	                		}
	                	}

	                	A = temp;

	                }

	                for (int k = 0; k < N; k++) {
	                	System.out.print(A[k] + " ");
	                }

	                System.out.println();

                }

        }

}