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 all(v) v.begin(), v.end()
using in = int64_t;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define REP(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define Yes cout<<"Yes"<<endl 
#define No cout<<"No"<<endl
#define yes cout<<"yes"<<endl 
#define no cout<<"no"<<endl
#define vec(a,y,x)  vector<vector<char>> a (y,vector<char>(x))
const double PI=3.14159265358979323846;
const in MOD = 1000000007;
const in INF=1e18+7;
const int inf=1e9+7;
const vector<int> dx={1,0,-1,0};
const vector<int> dy={0,1,0,-1};
//考察用
int main(){
  int n;
  int k;
  cin>>n>>k;
  vector<int> A(n);
  rep(i,n)
    cin>>A.at(i);
  
  //rep(m,k+1){//
    //cout<<m<<": ";
  int m=k;
  vector<int> a=A;
  rep(i,m){
    vector<int> b(n,0);
    rep(j,n){
      for(int m=-1*a.at(j);m<=a.at(j);m++){
        if(j+m<0||j+m>=n) continue;
        b.at(j+m)++;
      }
    }
    a=b;
  }
  rep(i,n)
    cout<<a.at(i)<<" ";
  cout<<endl;
  //}//
}