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;

#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define int long long

const int N=2e5+5;

void solve()
{	
	int n,k;
	cin>>n>>k;
	int a[n+5];

	for(int i=1;i<=n;i++)
		cin>>a[i];
	
	for(int j=1;j<=k;j++)
	{
		bool flag=true;
		for(int i=1;i<=n;i++)
		{
			if(a[i]!=n)
				flag=false;
		}	
		if(flag)
			break;
		int prev[n+5];
		for(int i=0;i<=n;i++)
			prev[i]=0;
		for(int i=1;i<=n;i++)
		{
			prev[max(1LL,i-a[i])]+=1;
			prev[min(n+1,i+a[i]+1)]-=1;
		}
		for(int i=1;i<=n;i++)
			prev[i]+=prev[i-1];
		for(int i=1;i<=n;i++)
			a[i]=prev[i];
	}
	for(int i=1;i<=n;i++)
		cout<<a[i]<<" ";
}

int32_t main()
{
	#ifndef ONLINE_JUDGE
	freopen("input.txt","r",stdin);
	freopen("output.txt","w",stdout);
	#endif
	
	IOS;

	int t=1;
	//cin>>t;
	while(t--)
		solve();

}