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: Accepted)

#include <bits/stdc++.h>
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
#define repi(i,start,end) for(int i=int(start);i<int(end);++i)
#define rep(i,n) repi(i,0,n)
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define v(T) vector<T>
#define vv(T) v(v(T))
#define vvv(T) v(v(v(T)))
typedef v(int) vi;
typedef pair<int,int> P;
template<class T> inline bool chmax(T& a,T b){if(a<b){a=b;return true;}return false;}
template<class T> inline bool chmin(T& a,T b){if(a>b){a=b;return true;}return false;}
template<typename T> ostream &operator<<(ostream &os, const vector< T > &v){
  rep(i,v.size()) os << v[i] << (i + 1 != int(v.size()) ? " " : "");
  return os;
}
template<typename T> istream &operator>>(istream &is, vector< T > &v){
  for(T &in : v) is >> in;
  return is;
}

v(int) update(v(int) X) {
  int n = X.size();
  v(int) A(n + 1,0);
  rep(i,n) {
    A[max(0, i - X[i])]++;
    A[min(n, i + X[i] + 1)]--;
  }
  v(int) B(n,0);
  B[0] = A[0];
  repi(i, 1, n){
    B[i] = B[i - 1] + A[i];
  }
  return B;
}

void Main()
{
  int N, K;
  cin >> N >> K;
  v(int) A(N);
  cin >> A;

  rep(i, min(K,100)) {
    A = update(A);
  }

  cout << A << "\n";
}

int main()
{
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  Main();
}