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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionC
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 整数配列の入力
            var inputLongArray = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            var n = inputLongArray[0];
            var k = inputLongArray[1];

            var a = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();

            //var denkyuuList = new List<denkyuu>();
            //for (int i = 0; i < a.Length; i++)
            //{
            //    var denkyuu = new denkyuu();
            //    denkyuu.x = i;
            //    denkyuu.d = a[i];

            //    denkyuuList.Add(denkyuu);
            //}

            //long sum = 0;
            //for (int i = 0; i < k; i++)
            //{
            //    var denkyuuList_new = new List<denkyuu>();
            //    foreach (var item in denkyuuList)
            //    {
            //        denkyuuList_new.Add(new denkyuu(item));
            //    }

            //    foreach (var item in denkyuuList)
            //    {
            //        item.d = denkyuuList_new.Count(x => item.x >= x.lightrange_min
            //                                            && item.x <= x.lightrange_max);
            //    }
            //    var sum2 = (long)denkyuuList.Sum(x => x.d);
            //    if (sum == sum2)
            //    {
            //        break;
            //    }
            //    sum = sum2;
            //}

            //string result = "";
            //for (int i = 0; i < denkyuuList.Count; i++)
            //{
            //    result += (i == 0 ? "" : " ") + denkyuuList[i].d.ToString();
            //}]

            var ans = a;
            for (int i = 0; i < k; i++)
            {
                var tmp = new int[n + 1];
                for (int j = 0; j < ans.Length; j++)
                {
                    tmp[Math.Max(0, j - ans[j])]++;
                    tmp[Math.Min(n, j + ans[j] + 1)]--;
                }

                for (int j = 0; j < ans.Length; j++)
                {
                    ans[j] = (j == 0 ? 0 : ans[j -1]) + tmp[j];
                }
                if (!ans.Any(x => x != n))
                {
                    break;
                }
            }

            Console.WriteLine(string.Join(" ",ans));
            Console.Out.Flush();
        }
        //public class denkyuu
        //{
        //    public denkyuu()
        //    {}
        //    public denkyuu(denkyuu _d)
        //    {
        //        x = _d.x;
        //        d = _d.d;
        //    }
        //    public int x { get; set; }
        //    public int d { get; set; }
        //    public int lightrange_min
        //    {
        //        get { return x - d; }
        //    }
        //    public int lightrange_max
        //    {
        //        get { return x + d; }
        //    }
        //}
    }
}