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: Accepted)

using System;
using System.Linq;

class C
{
	static int[] Read() => Console.ReadLine().Split().Select(int.Parse).ToArray();
	static void Main()
	{
		var h = Read();
		int n = h[0], k = h[1];
		var a = Read();

		for (int c = 0; c < k; c++)
		{
			var d = new int[n];
			for (int i = 0; i < n; i++)
			{
				d[Math.Max(0, i - a[i])]++;
				if (i + a[i] + 1 < n) d[i + a[i] + 1]--;
			}
			for (int i = 1; i < n; i++)
				d[i] += d[i - 1];

			if (Enumerable.SequenceEqual(a, d)) break;
			a = d;
		}
		Console.WriteLine(string.Join(" ", a));
	}
}