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<stdlib.h>

void main(){
  long N,K;
  long n;
  long k,j;
  long *A,*AA;
  int dm;
  dm=scanf("%ld %ld",&N,&K);
  A = (long*)malloc(sizeof(long)*N);
  AA = (long*)malloc(sizeof(long)*N);
  for(n=0;n<N;n++){
  	dm=scanf("%ld", A + n);
  }

  for(k=0;k<K;k++){
    for(n=0;n<N;n++){
      AA[n]++;
      if(A[n] > 0){
        for(j=0;j<A[n];j++){
          if(N > n + j + 1){ 
            AA[n + j + 1]++;
          }
          if(n >= j + 1){
            AA[n - j - 1]++;
          }
      }
    }
  }
    for(j=0;j<N;j++){
      A[j] = AA[j];
      AA[j] = 0;
    }
  }
  for(j=0;j<N;j++){
  	printf("%d ", A[j]);
  }
  printf("\n");
}