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;

using ll = long long;

#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()
#define len(x) int((x).size())

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	#ifdef ARTHUR_LOCAL
		ifstream cin("input.txt");
	#endif

	int n,k;
	cin>>n>>k;

	vector<int> A;

	for(int i=0; i<n; i++)
	{
		int a;
		cin>>a;
		A.push_back(a);
	}

	while(k--)
	{
		vector<int> new_A(n);
		priority_queue<int> PQ;
		int cur=0;

		for(int i=0; i<n; i++)
		{
			cur++;
			PQ.push(-i-A[i]);

			while(!PQ.empty() && -PQ.top()<i)
			{
				cur--;
				PQ.pop();
			}

			new_A[i]+=cur;
			//cout << i << " " << cur << endl;
		}

		while(!PQ.empty()) PQ.pop();
		cur=0;
		bool fin=1;

		//cout << endl;

		for(int i=n-1; i>=0; i--)
		{
			cur++;
			PQ.push(i-A[i]);

			while(!PQ.empty() && i<PQ.top())
			{
				cur--;
				PQ.pop();
			}

			new_A[i]+=cur-1;
			if(new_A[i]!=n) fin=0;
		
			//cout << i << " " << cur << endl;
		}

		//cout << endl;

		A=new_A;
		if(fin) break;
	}

	for(auto a:A) cout << a << " ";
	cout << "\n";
}