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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;

class Program
{
	static void Main(string[] args)
	{
		string[] strInput = Console.ReadLine().Split(' ');
		Int64 n = Int64.Parse(strInput[0]);
		Int64 k = Int64.Parse(strInput[1]);
		strInput = Console.ReadLine().Split(' ');

		Int64[] a = new Int64[n];
		int i, j, l;
		for(i = 0; i < n; i++)
		{
			a[i] = Int64.Parse(strInput[i]);
		}

		

		for (i = 0; i < k; i++)	//操作回数
		{
			Int64[] new_a = new Int64[n];

			for (j = 0; j < n; j++)	//全電球
			{
				for(l = 0; l < n; l++)	//ある電球に対する全電球の影響
				{
					if(Math.Abs(j - l) <= a[l])
					{
						new_a[j]++;
					}
				}
			}

			Array.Copy(new_a, a, a.Length);
		}

		Console.WriteLine(string.Join(" ", a));
		return;
	}
}