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


int main(){
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  int  n,k;
  cin>>n>>k;
  int a[200005];
  int b[200005];
  for(int i=0;i<n;i++){
    cin>>a[i];
    b[i]=0;
  }
  b[n]=0;
  int d=min(50,k);
 
  for(int j=0;j<d;j++){
  for(int i=0;i<n;i++){
    int l=max(0,i-a[i]);
    int r=min(n,i+a[i]+1);
    b[l]++;
    b[r]--;
  }
    for(int i=1;i<n;i++){
     b[i]+=b[i-1];
      
    }
    for(int i=0;i<n;i++){
    a[i]=b[i];
      b[i]=0;
    }
   
  }
 
  
  for(int i=0;i<n;i++){
  cout<<a[i]<<" ";
  }
  






}