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: Time Limit Exceeded)

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

int main(){
  int N,K,flag;
  cin>>N>>K;
  vector<int>A(N,0);
  vector<int>B(N,0);
  for(int i=0;i<N;i++){
    cin>>A[i];
  }
  
  if(K>100){
    for(int i=0;i<N-1;i++){
      cout<<N<<" ";
    }
    cout<<N<<endl;
    return 0;
  }
  
  while(K){   
    
    for(int i=0;i<N;i++){
      if(A[i]==N){
        for(int l=0;l<N;l++){
          B[l]++;
        }
        B[i]=N;
        continue;
      }

      for(int j=i-A[i];j<=i+A[i];j++){
        if(j>=0 && j<=N-1){
          B[j]++;
          if(B[j]>N){
            B[j]=N;
          }
        }
      }  
    }
    flag=1;
    for(int k=0;k<N;k++){
      if(B[k]<N) flag=0;
      A[k]=B[k];
      B[k]=0;  
      }
    if(flag) break;
    
    K--;
    
    /*for(int p=0;p<N-1;p++){
      cout<<A[p]<<" ";
    }
    cout<<A[N-1]<<endl;*/
    
  }
  
  if(flag){
    for(int i=0;i<N-1;i++){
      cout<<N<<" ";
    }
    cout<<N<<endl;
    return 0;
  }
  
  for(int p=0;p<N-1;p++){
    cout<<A[p]<<" ";
  }
  cout<<A[N-1]<<endl;
  return 0;
}