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<string.h>
//#include<stdlib.h>
#include<math.h>

int main(void){
  int N,K;
  int i,j,m,n;
  scanf("%d %d",&N,&K);
  int A[N];
  int B[N];
  for(i = 0;i < N;i++){
    scanf("%d",&A[i]);
    B[i] = 0;
  }
  for(i = 0;i < K ;i++){
    for(n = 0;n < N;n++){
      B[n] = 0;
    }
    for(j = 0;j< N;j++){
      for(m = j - A[j] + 1;m <= j + A[j] + 1;m++){
        if(m <= 0 || m - 1 >= N){
          continue;
        }
        B[m - 1]++;
      }
    }
    for(n = 0;n < N;n++){
      A[n] = B[n];
    }
  }

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