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 AtCoder.Question
{
    public class QuestionC
    {
        public static void Main(string[] args)
        {
            var (n, k) = ReadHelper.ReadValue<long, long>();
            var ai = ReadHelper.ReadValues<long>();
            for (int i = 0; i < k; i++)
            {
                var next = new long[ai.Length];
                for (int j = 0; j < ai.Length; j++)
                {
                    var power = ai[j];
                    var left = j - power;
                    var right = j + power;
                    var indexes = Enumerable.Range((int)left, (int)(right - left + 1)).Where(x => 0 <= x && x < ai.Length).ToArray();
                    foreach (var index in indexes)
                    {
                        next[index]++;
                    }
                }
                ai = (long[])next.Clone();
            }
            Console.WriteLine(String.Join(' ', ai));
        }

        static class ReadHelper
        {
            internal static T ReadValue<T>()
            {
                return (T)Convert.ChangeType(Console.ReadLine(), typeof(T));
            }
            internal static (T1, T2) ReadValue<T1, T2>()
            {
                var input = Console.ReadLine().Split(' ');
                return ((T1)Convert.ChangeType(input[0], typeof(T1)), (T2)Convert.ChangeType(input[1], typeof(T2)));
            }
            internal static (T1, T2, T3) ReadValue<T1, T2, T3>()
            {
                var input = Console.ReadLine().Split(' ');
                return ((T1)Convert.ChangeType(input[0], typeof(T1)), (T2)Convert.ChangeType(input[1], typeof(T2)), (T3)Convert.ChangeType(input[2], typeof(T3)));
            }
            internal static (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>()
            {
                var input = Console.ReadLine().Split(' ');
                return ((T1)Convert.ChangeType(input[0], typeof(T1)), (T2)Convert.ChangeType(input[1], typeof(T2)), (T3)Convert.ChangeType(input[2], typeof(T3)), (T4)Convert.ChangeType(input[3], typeof(T4)));
            }
            internal static T[] ReadValues<T>()
            {
                var input = Console.ReadLine().Split(' ');
                return input.Select(x => (T)Convert.ChangeType(x, typeof(T))).ToArray();
            }
        }

        static class MathAlgorithm
        {
            internal static bool IsPrime(long n)
            {
                if (n == 2) return true;
                if (n < 2 || n % 2 == 0) return false;
                var sqrt = Math.Sqrt(n);
                for (int i = 3; i <= sqrt; i += 2) if (n % i == 0) return false;
                return true;
            }
            internal static IEnumerable<long> EnumeratePrimes(long n)
            {
                var i = 2L;
                while (i * i <= n)
                {
                    if (n % i == 0)
                    {
                        n /= i;
                        yield return i;
                    }
                    else
                    {
                        i += i == 2 ? 1 : 2;
                    }
                }
                if (n != 1) yield return n;
            }
        }
    }
}