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>
#define rep(i,n) for(int i=0;i<(n);++i)
using namespace std;
using ll=long long;
int i,j,n,c=1,k;
int main(){
  cin>>n>>k;
  vector<ll> a(n);
  vector<ll> b(n);
  rep(i,n)cin>>a[i];
  bool f=false;
  while(c<=k){
    rep(i,n)b[i]=0;
    rep(i,n){
      ll idx=max(ll(0),i-a[i]);
      for(;idx<min(ll(n),i+a[i]+1);++idx){
        b[idx]++;
      }
    }
    rep(i,n)a[i]=b[i];
    c++; 
    if(c>20){f=true;break;}
  }
  if(f)rep(i,n)cout<<n<<" ";
  else rep(i,n)cout<<a[i]<<" ";
}