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 ProblemC
{
    class Program
    {
        static int[] initAs;
        static void Main(string[] args)
        {
            var read = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var N = read[0];
            var K = read[1];
            initAs = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            
            var res = Solve(N, K, initAs);
            Console.WriteLine(String.Join(" ", res));
        }

        static int[] Solve(int N, int K, int[] initAs)
        {
            var res = initAs;
            for (int i = 0; i < K; i++)
            {
                res = GetBs(res, N);
                if (res.All(x => x >= N))
                    break;
            }
            return res;
        }

        static int[] GetBs(int[] As, int N)
        {
            var Bs = new int[N];
            for (int i = 0; i < As.Length; i++)
            {
                var l = Math.Max(0, i - As[i]);
                var r = Math.Min(N - 1, i + As[i]);
                Bs[l]++;
                if (r + 1 < N) Bs[r + 1]--;
            }
            for (int i = 1; i < Bs.Length; i++)
            {
                Bs[i] += Bs[i - 1];
            }
            return Bs;
        }

        //static void Solve(int K, ref int[] As)
        //{
        //    if (K == 0)
        //        As = initAs;
        //    else
        //    {
        //        Solve(K - 1, ref As);
        //        for (int i = 0; i < length; i++)
        //        {

        //        }
        //    }
        //}
    }
}