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 <bits/stdc++.h>

using namespace std;

int main()
{
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> a(n);
  for (int i = 0; i < n; i++)
  {
    cin >> a[i];
  }
  vector<int> b(n + 1);
  while (k--)
  {
    for (int i = 0; i <= n; i++)
    {
      b[i] = 0;
    }
    for (int i = 0; i < n; i++)
    {
      int from = max(i - a[i], 0);
      int to = min(i + a[i], n - 1);
      b[from] += 1;
      b[to + 1] -= 1;
    }
    // for (int i = 0; i <= n; i++)
    // {
    //   cout << b[i] << " ";
    // }
    // cout << endl;
    bool changed = false;
    for (int i = 0; i < n; i++)
    {
      if (a[i] != b[i])
        changed = true;
      a[i] = b[i];
      b[i + 1] += b[i];
    }
    if (!changed)
    {
      break;
    }
  }
  for (int i = 0; i < n; i++)
  {
    if (i > 0)
    {
      cout << " ";
    }
    cout << a[i];
  }
  cout << '\n';
  return 0;
}