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.*;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
      	int K = sc.nextInt();
      	if(K>100) K=41;
     	Integer A[] = new Integer[N];
      	Integer ans[] = new Integer[N];
        for (int i=0; i<N; i++) {
            A[i] = sc.nextInt();
          	ans[i] = 1;
        }
      
      	for(int con=0; con<K; con++){
          for(int i=0; i<N;i++){
            int sta = 0;
            int end = N-1;
            if(i-A[i]>0) sta=i-A[i];
            if(i+A[i]<N-1) end=i+A[i];
            for(int j=sta;j<=end;j++) {
            	if(j != i) ans[j] += 1;
            }
          }
          //System.out.println(Arrays.asList(ans));
          for (int i=0; i<N; i++) {
            A[i] = ans[i];
            ans[i] = 1;
          }
        }  
          
      	//System.out.println(Arrays.asList(A));
      	for (int i=0; i<N; i++) {
            System.out.println(A[i]);
        }
      	
    }
}