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>
#include <string> 

using namespace std;
string N;
int A[200010]{};
int a[200010]{};
void sum(int x,int d,int* f){
    for(int j=x-d;j<x+d+1;j++){
      if(j>0&&200010>j)f[j]++;
    }
}
int main()
{
  int N,K;
  cin>>N>>K;
  for(int i=1;i<N+1;i++){
    scanf("%d",&A[i]);
  }

  int k;
  for(k=1;k<K+1;k++){
    if(k%2!=0){
      for(int i=1;i<N+1;i++)a[i]=0;
    }else {
      for(int i=1;i<N+1;i++)A[i]=0;
    }
    for(int i=1;i<N+1;i++){
      if(k%2!=0){
        sum(i,A[i],a);
      }else {
        sum(i,a[i],A);
      }
    }
  }
  if(k%2!=0)for(int i=1;i<N+1;i++)printf("%d ",A[i]);
  else for(int i=1;i<N+1;i++)printf("%d ",a[i]);
  return 0;
}