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>
int main(void)
{
  int n,k;
  scanf("%d %d",&n,&k);
  int a[300000];
  int tmp[300000];

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


  while(k-->0){
    int flag=0;
    for(int i=0;i<n;i++){
      tmp[i]=0;
    }

    for(int i=0;i<n;i++){
      int min=i-a[i];
      if(i-a[i]<0){
        min=0;
      }
      tmp[min]++;
      int max=i+a[i];
      if(max>n-1){
        max=n-1;
      }
      if(max+1<n){
        tmp[max+1]--;
      }
    }
    for(int i=0;i<n;i++){
      if(i!=0){
        tmp[i]+=tmp[i-1];
      }
      if(a[i]!=tmp[i]){
        flag=0;
      }
      a[i]=tmp[i];
    }
    if(flag==1)break;
  }


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

  return 0;
}