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;
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 => long.Parse(i)).ToArray();
            long N = inputLongArray[0];
            long K = inputLongArray[1];
            var lightCount = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();

            for (long i=0; i<K; i++)
            {
                var tmp = new List<Entity>();
                for (long j = 0; j < N; j++)
                {
                    long curLight = lightCount[j];
                    tmp.Add(new Entity { min = j - curLight, max = j + curLight });
                }
                for (long j = 0; j < N; j++)
                {
                    lightCount[j] = tmp.Where(p => p.min <= j && j <= p.max).LongCount();
                }
            }
            Console.WriteLine(string.Join(" ", lightCount));

            Console.Out.Flush();
        }

        public class Entity {
            public long min { get; set; }
            public long max { get; set; }
        }

    }
}