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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int N,K;
  cin >> N >> K;
  vector<vector<int>> data(K+1, vector<int>(N));
  for (int i = 0; i < N; i++) 
  {
    cin >> data.at(0).at(i);
  }
  for (int j = 0; j < K; j++)
  {
    for (int i = 0; i < N; i++) 
    {
      for( int k = 0; k < 1 + data.at(j).at(i); k++){
        if( j+1 <= K && i+k <= N-1){
          data.at(j+1).at(i+k)++;
        }
      }
      for( int k = 0; k < 1 + data.at(j).at(i); k++){
        if(k >= 1 && i-k >= 0){
          data.at(j+1).at(i-k)++;
        }
      }              
    }
  }
  
    
    for (int i = 0 ; i < N; i++){
      cout << data.at(K).at(i);
    }

  
}