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;
#define rep(i,n) for(int i=0; i<(n); i++)
#define all(v) v.begin(), v.end()
//
vector<int> light(vector<int> v){
   int N=v.size();
   vector<int> vv(N,0);
   rep(i,v.size()){
      int a,b;
      a=max(0,(i-v[i]));
      b=min(N-1,i+v[i]);
      for(int j=a;j<=b;j++){
         vv[j]++;
      }
   }
   return vv;
   
}

int main(){
   int N,K;
   cin>>N>>K;
   vector<int> v;
   if(K>2*N){
      vector<int> vv(N,N);
      for(auto e:v) cout<<e<<" ";
      cout<<endl;
   } 
   rep(i,N){
      int a;
      cin>>a;
      v.push_back(a);
   }
   rep(i,K){
      v=light(v);
      
   }
   for(auto e:v) cout<<e<<" ";
   cout<<endl;
}