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[] a = new int[n];

        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }

        if(k > 31){
            StringBuilder sb = new StringBuilder();
            for(int i = 0; i < n; i++){
                sb.append(n).append("\n");
            }
            System.out.print(sb.toString());
            return;
        }

        for(int i = 0; i < k; i++){
            int[] b = new int[n];
            for(int j = 0; j < n; j++){
                b[j] += 1;
                for(int l = 1; l <= a[j]; l++){
                    if(j - l >= 0){
                        b[j - l] += 1;
                    }
                    if(j + l < n){
                        b[j + l] += 1;
                    }
                }
            }
            a = b;
        }

        StringBuilder sb = new StringBuilder();
        for(int i : a) {
            sb.append(i).append("\n");
        }
        System.out.print(sb.toString());

    }
}