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;
  cin>>n>>k;
  vector<long int> a(n),b(n);
  for(int i=0;i<n;i++){
    cin>>a.at(i);
    b.at(i)=0;
  }
  for(int l=1;l<=k;l++){
    for(int i=0;i<n;i++){
      int p=i-a.at(i),q=i+a.at(i);
      if(p<0)p=0;
      if(q>n-1)q=n-1;
      for(int j=p;j<=q;j++){
        b.at(j)++;
      }
    }
    int judge=0;
    for(int i=0;i<n;i++){
      a.at(i)=b.at(i);
      b.at(i)=0;
      if(a.at(i)==n) judge++;
    }
    if(judge==n)break;
  }
  for(int i=0;i<n;i++) {
    cout<<a.at(i)<<" ";
  }
}