#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

int main(){
  int N, K;
  cin >> N >> K;
  vector<int> A(N+1);
  for(int i = 0; i < N; ++i)
    cin >> A[i];

  for(int i = 0; i < K; ++i){
    vector<int> B(N+1);
    for(int j = 0; j < N; ++j){
      int d = A[j];
      ++B[max(0,j-d)];
      --B[min(N,j+d+1)];
    }
    int mi = N;
    for(int j = 0; j < N; ++j){
      B[j+1] += B[j];
      mi = min(mi,B[j]);
    }
    swap(B,A);
    if(mi >= N) break;
  }
  for(int i = 0; i < N; ++i)
    cout << A[i] << (i+1 < N ? " " : "\n");
}

### Prompt

Create a solution in cpp for the following problem:

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

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

Examples

Input

5 1
1 0 0 1 0


Output

1 2 2 1 2


Input

5 2
1 0 0 1 0


Output

3 3 4 4 3

### Response

```cpp
#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

int main(){
  int N, K;
  cin >> N >> K;
  vector<int> A(N+1);
  for(int i = 0; i < N; ++i)
    cin >> A[i];

  for(int i = 0; i < K; ++i){
    vector<int> B(N+1);
    for(int j = 0; j < N; ++j){
      int d = A[j];
      ++B[max(0,j-d)];
      --B[min(N,j+d+1)];
    }
    int mi = N;
    for(int j = 0; j < N; ++j){
      B[j+1] += B[j];
      mi = min(mi,B[j]);
    }
    swap(B,A);
    if(mi >= N) break;
  }
  for(int i = 0; i < N; ++i)
    cout << A[i] << (i+1 < N ? " " : "\n");
}

```