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 kaijouC
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int K = int.Parse(input[1]);
            string[] Array = Console.ReadLine().Split(' ');
            int[] A = new int[N];
            for(int i = 0; i < N; i++)
            {
                A[i] = int.Parse(Array[i]);
            }
            for(int i = 0; i < 20 & i < K; i++)
            {
                int[] Atemp = new int[N];
                for (int j = 0; j < N; j++)
                {
                    int min = j - A[j];
                    int max = j + A[j];
                    if (min < 0)
                    {
                        min = 0;
                    }
                    if (max >= N)
                    {
                        max = N - 1;
                    }
                    for (int k = min; k <= max; k++)
                    {
                        Atemp[k] += 1;
                    }
                }
                for (int j = 0; j < N; j++)
                {
                    A[j] = Atemp[j];
                }
            }

            string[] ans = new string[N];
            for(int i = 0; i < N; i++)
            {
                ans[i] = A[i].ToString();
            }
            Console.WriteLine(string.Join(" ",ans));
        }
    }
}