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;
using System.IO;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        int[] nk = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        int n = nk[0];
        int k = nk[1];
        int[] a = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        for (int h = 0; h < k; h++)
        {
            int[] aa = Enumerable.Repeat(1, n).ToArray();
            for (int i = 0; i < n; i++)
            {
                if (a[i] == 0) continue;
                try
                {
                    for (int j = i - 1; i - 1 - a[i] < j; j--)
                        aa[j]++;
                }
                catch (IndexOutOfRangeException) { }
                try
                {
                    for (int j = i + 1; j < i + 1 + a[i]; j++)
                        aa[j]++;
                }
                catch (IndexOutOfRangeException) { }
            }
            a = aa;
        }
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        for (int i = 0; i < n; i++)
            Console.Write(a[i] + " ");
        Console.Out.Flush();
    }
}