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.Collections.Generic;
using System.Linq;

namespace TokyoKaizyo
{
    class ProgramC
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine();
            var inputList = input.Split(" ");
            int.TryParse(inputList[0], out var n);
            int.TryParse(inputList[1], out var k);

            var input2 = Console.ReadLine();
            var luxList = input2.Split(" ").Select(int.Parse).ToArray();

            for (var i = 0; i < 42 && i < k; i++)
            {
                var dic = new Dictionary<int, int>();
                for (var j = 0; j < n; j++)
                {
                    dic.Add(j, 0);
                }


                for (var j = 0; j < n; j++)
                {
                    var lux = luxList[j];
                    var start = Math.Max(0, j - lux);
                    var end = Math.Min(n - 1, j + lux);

                    for (var c = start; c <= end; c++)
                    {
                        dic[c]++;
                    }
                }

                luxList = dic.OrderBy(d => d.Key).Select(d => d.Value).ToArray();
            }

            Console.WriteLine(string.Join(" ", luxList));
        }
    }
}