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 <iostream>
#include <vector>
#include <algorithm>

int main(){
 int N,K;
 std::cin>>N>>K;
 std::vector<int> A(N);
 for(int i=0;i<N;i++){
  std::cin>>A[i];
 }
 
 for(int i=0;i<K;i++){
  int flag=1;
  for(int i=0;i<N;i++){
   if(A[i]!=N){
    flag=0;
    break;
   }
  }
  if(flag){
   break;
  }
  std::vector<int> B(N,0);
  for(int i=0;i<N;i++){
   int l=std::max(0,i-A[i]);
   int r=std::min(N-1,i+A[i]);
   B[l]++;
   if(r+1<N) B[r+1]--;
  }
  for(int i=1;i<N;i++) B[i]+=B[i-1];
  A=B;
 }
 for(int i=0;i<N;i++){
  std::cout<<A[i]<<" ";
 }
 std::cout<<std::endl;

 return 0;
}