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: Wrong Answer)

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<algorithm>
#include<cstring>
using namespace std;
int a[200005]={0},b[200005]={0};
int main()
{
	int n,k,l,r,cnt=0;
	cin >> n >> k;
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
	}
	for(int i=1;i<=k;i++){
		cnt=0;
		for(int j=1;j<=n;j++){
			if(a[j]==n)
				cnt++;
		}
		if(cnt==n)break;
		memset(b,0,sizeof(b));
		for(int j=1;j<=n;j++){
			l=j-a[j];
			r=j+a[j];
			if(l<1)l=1;
			if(r>n)r=n;
			b[l]++;
			if(r+1<=n)
				b[r+1]--;
		}
		for(int j=2;j<=n;j++){
			b[j]+=b[j-1];
		}
		for(int j=1;j<=n;j++){
			a[j]=b[j];
		}
	}
	for(int i=1;i<=n;i++){
		printf("%d ",b[i]);
	}
	return 0;
}