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.Linq;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            String[] N_K = Console.ReadLine().Split(' ');
            String[] strAs = Console.ReadLine().Split(' ');
            int N = int.Parse(N_K[0]);
            int K = int.Parse(N_K[1]);
            int[] As = new int[N];
            for(int i = 0; i < N; i++) As[i] = int.Parse(strAs[i]);

            for(int i = 0; i < K; i++) {
                int[] lights = Enumerable.Repeat(0, N).ToArray();
                for(int j = 0; j < N; j++) {
                    if(As[j] == 0) {
                        lights[j]++;
                    } else {
                        for(int k = Math.Max(0, j-As[j]); k < Math.Min(N, j+As[j]+1); k++){
                            lights[k]++;
                        }
                    }
                }
                As = lights.Clone() as int[];
            }

            for(int i = 0; i < N; i++) strAs[i] = As[i].ToString();
            Console.WriteLine(String.Join(' ', strAs));
        }
    }
}