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.*;
 
public class Main {
 
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int K = sc.nextInt();
		long[] A = new long[N];
		for (int i = 0; i < N; i++) {
			A[i] = sc.nextInt();
		}
		for (int i = 0; i < K; i++) {
			A = calc(A);
		}
		StringBuilder sb = new StringBuilder();
		for (long ans : A) {
			sb.append(ans).append(" ");
		}
		System.out.println(sb);
	}
	
	private static long[] calc(long[] ar) {
		long[] res = new long[ar.length];
		for (int i = 0; i < ar.length; i++) {
			for (int j = 0; j <= ar[i]; j++) {
				if (j == 0) {
					res[i]++;
				} else {
					if (-1 < i-j) {
						res[i-j]++;
					}
					if (i+j < res.length) {
						res[i+j]++;
					}	
				}
			}
		}
		return res;
	}
}