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.*; 
import java.lang.*; 


public class Main{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
                
                int N = scan.nextInt();
                int K = scan.nextInt();
                ArrayList<Integer> light = new ArrayList<>();
                ArrayList<Integer> ans = new ArrayList<>();
                ArrayList<Integer> ans2 = new ArrayList<>();
                for(int i=0; i<N; i++){
                    int A = scan.nextInt();
                    light.add(A);
                    ans.add(0);
                    ans2.add(0);
                }
                
                int kai = 0;
                while(kai<K){
                    for(int m=0; m<N;m++){
                        for(int j=-light.get(m); j<=light.get(m); j++){
                            if(0<=m+j && m+j<N){
                                ans.set(m+j,ans.get(m+j)+1);
                            }
                        }
                    }
                    
                    int cnt = 0;      
                    for(int k=0; k<N; k++){
                        if(ans.get(k)==N){
                            cnt++;
                        }
                        light.set(k, ans.get(k)-ans2.get(k));
                        ans2.set(k, ans.get(k));
                    }
                    if(cnt==N){
                        for(int k=0; k<N; k++){
                             System.out.print(light.get(k)+" ");
                          }
                        System.exit(0);
                    }
                    kai++;
                }
                for(int k=0; k<N; k++){
                    System.out.print(light.get(k)+" ");
                }
        }
}