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: Output Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

int cmp(const void * n1, const void * n2){
  if(*(double *) n1 > *(double *) n2){
    return 1;
  }else if (*(double *) n1 < *(double *) n2){
    return -1;
  }else{
    return 0; 
  }
}

int main(){
    int n,k;
    scanf("%d %d", &n, &k);
    int arr[n];
    double t1[n], t2[n];
    for(int i=0;i<n;i++)scanf("%d",&arr[i]);
  
    for(int i=0;i<k;i++){
      for(int j=0;j<n;j++){
        t1[j] = j - arr[j] - 0.5;
        t2[j] = j + arr[j] + 0.5;
      }
      qsort(t1, sizeof(t1)/sizeof(t1[0]), sizeof(double), cmp);
      qsort(t2, sizeof(t2)/sizeof(t2[0]), sizeof(double), cmp);

      for(int l=0;l<n;l++)printf("%d ",arr[l]);
      printf("\n");
      for(int l=0;l<n;l++)printf("%d ",t2[l]);
      printf("\n");

      int tmp = 0;
      int k = 0;
      int h = 0;
      for(int j=0;j<n;j++){
        int tmpk = 0;
        int tmph = 0;
        while (k < n && t1[k] <= j) {k++;tmpk++;}
        while (h < n && t2[h] < j) {h++;tmph++;}
        tmp = tmp + tmpk - tmph;
        arr[j] = tmp;
      }
    }
    for(int l=0;l<n;l++)printf("%d ",arr[l]);
    return 0;
}