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.Scanner;

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

		// 整数の入力
		int n = sc.nextInt();
		int k = sc.nextInt();
		int a[] = new int[n];
		
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		
		for (int i = 0; i < k; i++) {
			int a2[] = new int[n];
			for(int j = 0; j < n; j++) {
				a2[j] = 0;
			}
			
			for (int j = 0; j < n; j++) {
				int l = j-a[j]>0?j-a[j]:0;
				int h = j+a[j]<n-1?j+a[j]:n-1;
				
				for (int o = l; o <= h; o++) {
					a2[o]++;
				}
			}
			
			a = a2;
			
			//for(int j = 0; j < n; j++) {
			//	a[j] = a2[j];
			//}
		}
		
		System.out.println(a);
		
		//for (int i = 0; i < n; i++) {
		//	System.out.printf("%d ", a[i]);
		//}
		
        sc.close();
	}
}