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>
#define NUM 200001

int main(void) {
  int N, K, i, j, k;
  int A[NUM], countA[NUM];
  
  scanf("%d %d", &N, &K);
  for(i = 0;i < N;i++)  scanf("%d", &A[i]);
  
  int bef, aft;
  
  for(k = 0;k < K;k++){
    for(i = 0; i < N; i++){
      bef = i - A[i];
      aft = i + A[i];
      for(j = bef; j <= aft; j++){
        if(j < 0) continue;
        if(j > N) break;
        countA[j]++;
      }
    }
    for(j = 0; j < N; j++){
      A[j] = countA[j];
      countA[j] = 0;
    }
  }
  
  for(i = 0; i < N; i++)  printf("%d ",A[i]);
  printf("\n");
      
  
  return 0;
}