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 C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>
int main(void){
  int i,j,p,q;
  int n,k;
  int a[200001]={0};
  int b[200001]={0};
  
  scanf("%d %d",&n,&k);
  for(i=0;i<n;i++){
   scanf("%d ",&a[i]); 
  }
  for(q=0;q<n;q++){
        b[q]=a[q];
      }
  
  
  for(i=0;i<k;i++){
    
    for(j=0;j<n;j++){
      
      
      
      b[j]=0;
      for(p=0;p<n;p++){
        if(a[p]>=abs(p-j)){
    		b[j]+=1;
        }
      }
      
      }
      for(q=0;q<n;q++){
        a[q]=b[q];
    }
    
    
    
  }
  
  
 for(i=0;i<n;i++){
   printf("%d ",a[i]); 
  }
  
  printf("\n");
  return 0;
}