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: Accepted)

#include <stdio.h>
#define max(x, y) ((x)<(y) ? (y) : (x))
#define min(x, y) ((x)>(y) ? (y) : (x))

int main(){
  int n, k;  scanf("%d %d", &n, &k);
  long a[200005];
  for(int i=1; i<=n; i++)  scanf("%ld", a+i);
  int flag = 0;
  for(int kk=0; kk<k; kk++){
    int thisflag = 1;
    long turn[200005] = {0};
    for(int i=1; i<=n; i++){
      turn[max(1, i-a[i])]++;
      turn[min(n+1, i+a[i]+1)]--;
    }
    long sum = 0;
    for(int i=1; i<=n; i++){
      sum += turn[i];
      a[i] = sum;
      if(n != a[i])
	thisflag = 0;
    }
    if(thisflag){
      flag = 1;
      break;
    }
  }
  
  if(flag)
    for(int i=1; i<=n; i++)
      printf("%d ", n);
  else
    for(int i=1; i<=n; i++)
      printf("%ld ", a[i]);
  puts("");
  return 0;
}