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: Runtime Error)

#include <iostream>
#include <string>
#include <vector>
#include <stdio.h>
#include <algorithm>
#define _USE_MATH_DEFINES
#include <cmath>
#include <numeric>
#include <iomanip>
#include <deque>
#include <tuple>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <sstream>
#include <stdexcept>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>

#define rep(i, x) for (int i = 0; i < (int)(x); i++)
#define FOR(i, a, done) for (int i = (a); i < (done); ++i)
#define all(a) (a).begin(), (a).end()
#define x first
#define y second
#define debug(a) cout << (a) << endl
namespace mp = boost::multiprecision;
using cpp_int = mp::cpp_int;
using ll = long long;
using namespace std;
template <class T>
bool chmax(T &a, const T &b)
{
	if (a < b)
	{
		a = b;
		return 1;
	}
	return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
	if (a > b)
	{
		a = b;
		return 1;
	}
	return 0;
}

ll M = 1000000007;

void solve()
{
	int n,k;
	cin>>n>>k;
	vector<int>a(n);
	vector<vector<int>>imos(k+2,vector<int>(n+2,0));
	rep(i,n){
		cin>>a[i];
		int mi=max(i-a[i],0);
		int ma=min(n-1,i+a[i]);
		imos[0][mi]++;
		imos[0][ma+1]--;
		
	}
	if((ll)n*k>=(ll)1e6 or n<=k){
		rep(i,n){
			cout<<n;
			if(i!=n-1){
				cout<<" ";
			}else{
				cout<<endl;
			}
		}
		return ;
	}
	int cur=0;
	rep(j,min(k,50)){
		cur=0;
		bool fin=true;
		rep(i,n){
			cur+=imos[j][i];
			a[i]=cur;
			int mi=max(i-a[i],0);
			int ma=min(n-1,i+a[i]);
			imos[j+1][mi]++;
			imos[j+1][ma+1]--;
			if(a[i]!=n){
				fin=false;
			}
		}
		if(fin){
			//cout<<j<<endl;
			rep(i,n){
				cout<<n;
				if(i!=n-1){
					cout<<" ";
				}else{
					cout<<endl;
				}
			}
			return ;
		}
	}
	rep(i,n){
		cout<<a[i];
		if(i!=n-1){
			cout<<" ";
		}else{
			cout<<endl;
		}
	}
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	solve();
	return 0;
}