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 <algorithm>
#include <cstdint>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#include <cfloat>

using namespace std;

using lint=int64_t;
using uint=uint32_t;
using ulint=uint64_t;

template<class T>
using vector2d=vector<vector<T>>;

template<class T>
bool UpdateMax(T &a, const T &b){
  if(a<b){
    a=b;
    return true;
  }else{
    return false;
  }
}

template<class T>
bool UpdateMin(T &a, const T &b){
  if(a>b){
    a=b;
    return true;
  }else{
    return false;
  }
}

template <class T>
void OutVec(const vector<T>& vec){
  for(int i = 0; i < vec.size() - 1; ++i){
    cout<<vec[i]<<" ";
  }
  cout<<vec.back()<<endl;
}

template <class T>
void OutVec2d(const vector2d<T>& vec){
  for(auto v:vec){
    OutVec(v);
  }
}

int main(){
  cout << std::fixed << std::setprecision(16);
  cin.tie(nullptr);
  std::ios::sync_with_stdio(false);

  int n,k;
  cin>>n>>k;
  vector<int> a(n);
  for(int i=0;i<n;i++){
    cin>>a[i];
  }

  for(int i=0;i<k;i++){
    vector<int> imos(n+1);
    for(int j=0;j<n;j++){
      int l=max(0,j-a[j]);
      int r=min(n,j+a[j]);
      imos[l]++;
      imos[r+1]--;
    }
    a[0]=imos[0];
    for(int j=0;j<n;j++){
      a[j]=a[j-1]+imos[j];
    }
    bool all_n=true;
    for(int j=0;j<n;j++){
      if(a[j]!=n){
        all_n=false;
        break;
      }
    }
    if(all_n){
      OutVec(a);
      return 0;
    }
  }
  OutVec(a);




  return 0;
}