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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;
public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
Scanner sc=new Scanner(System.in);
int N=sc.nextInt();
int K=sc.nextInt();
int A[]=new int[N];
int B[]=new int[N];

for(int i=0;i<N;i++)
{
 A[i]=sc.nextInt();
B[i]=0;
}
for(int l=0;l<K;l++)
{
for(int i=0;i<N;i++)
{
 for(int j=0;j<N;j++)
 {
	 if(i-A[i]-0.5<j && j < i+A[i]+0.5)
	 B[j]++;
 }
}
 for(int k=0;k<N;k++)
	{
		A[k]=B[k];
		B[k]=0;
	}

}
for(int k=0;k<N;k++)
{

System.out.println(	A[k]);
}
	}

}