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;
int A[200100],B[200100];
priority_queue<int,vector<int>,greater<int> > PQ1;
priority_queue<int,vector<int>,less<int> > PQ2;
int main()
{
	int N,K;
	cin>>N>>K;
	for(int i=0;i<N;i++)
		cin>>A[i];
	while(K--)
	{
		while(!PQ1.empty())
			PQ1.pop();
		for(int i=0;i<N;i++)
		{
			PQ1.push(i+A[i]);
			while(PQ1.top()<i)
				PQ1.pop();
			B[i]=(int)(PQ1.size());
		}
		while(!PQ2.empty())
			PQ2.pop();
		for(int i=N-1;i>=0;i--)
		{
			PQ2.push(i-A[i]);
			while(PQ2.top()>i)
				PQ2.pop();
			B[i]+=(int)(PQ2.size());
			B[i]--;
		}
		bool OK=true;
		for(int i=0;i<N;i++)
		{
			if(B[i]!=N)
				OK=false;
			A[i]=B[i];
		}
		if(OK)
			break;
	}
	for(int i=0;i<N;i++)
		cout<<A[i]<<" ";
	return 0;
}