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++ (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#define N 200001
#include <iostream>
using namespace std;

int main()
{
  int n, k, a[N], b[N] = {0}, i;
  cin >> n >> k;
  
  for (i=0; i<n; i++)
    cin >> a[i];
  
  i = 0;
  while (1)
  {
    for (int j=0; j<n; j++)
    {
      b[j] += 1;
      for (int l=1; l<=a[j]; l++)
      {
        if (j-l >= 0) b[j-l] += 1;
        if (j+l <  n) b[j+l] += 1;
      }
    }
    
    i += 1;
    if (i == k)
      break;
    
    for (int j=0; j<n; j++)
    {
      a[j] = b[j];
      b[j] = 0;
    }
  }
  
  i = 0;
  while (true)
  {
    cout << b[i];
    i += 1;
    if (i == n)
      return 0;
    cout << " ";
  }
}