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 (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int main(){
  int n,k;
  scanf("%d %d",&n,&k);

  int a[n],i;
  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
  }

  double b[n][2];
  int j,l,s=0;
  for(l=0;l<k;l++){
    for(i=0;i<n;i++){
      b[i][0]=i+1-a[i]-0.5;
      b[i][1]=i+1+a[i]+0.5;
    }
    for(i=1;i<=n;i++){
      for(j=0;j<n;j++){
        if(b[j][0]<i && i<b[j][1]){
          s++;
        }
      }
      a[i-1]=s;
      s=0;
    }
  }

  for(i=0;i<n;i++){
    printf("%d ",a[i]);
  }
  printf("\n");
  return 0;
}