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>
using namespace std;
typedef long long LL;
#define fi first
#define se second
#define pb push_back
#define forn(i,n) for(int i=0;i<(n);i++)
#define for1(i,n) for(int i=1;i<=n;i++)
#define forr(i,n) for(int i=n;i>=0;i--)
#define all(x) x.begin(), x.end()
const int MAXN = 2e5 +5;

void fio(){
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
LL n;
LL bit[MAXN];

template <typename A, typename B>
string to_string(pair<A, B> p);
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
 
string to_string(const string& s) {
  return '"' + s + '"';
}
 
string to_string(const char* s) {
  return to_string((string) s);
}
 
string to_string(bool b) {
  return (b ? "true" : "false");
}
 
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
 
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
 
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}


void debug_out() { cerr << endl; }
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)



void up(LL x, LL v){
	while(x<=(n)){
		bit[x]+=v;
		x+=x&-x;
	}
}

LL qu(LL x){
	LL su = 0;
	while(x>0){
		su+=bit[x];
		x-=x&-x;
	}
	return su;
}

LL k;
int main(){
  fio();
  cin>>n>>k;
  vector<LL> a(n+1);
  for1(i,n) {
  	cin>>a[i];
  	LL l = max(1LL, i - a[i]);
  	LL r = min(n, i+a[i])+1;
  	up(r,-1);
  	up(l,+1);
  }
  k = min(100LL, k);

  vector<LL> an(n+1);
  while(k){
  	 //cout<<"yes"<<endl;
	  for1(i,n) an[i] = qu(i);
	  //debug(an);
	  memset(bit, 0 ,sizeof bit);
	  for1(i,n){
	  	LL l = max(1LL, i - an[i]);
	  	LL r = min(n, i+an[i])+1;
	  	up(r,-1);
	  	up(l,+1);
	  }
	  k--;
	}
  for1(i,n) cout<<an[i]<<" ";
  cout<<endl;
  return 0;
}