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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Text;

namespace ABC0613
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] inp = Console.ReadLine().Split(' ');
            int n = int.Parse(inp[0]);
            int k = int.Parse(inp[1]);
            string[] light = Console.ReadLine().Split(' ');
            var lights = new List<int>();

            for (int i = 0; i < n; i++)
            {
                lights.Add(int.Parse(light[i]));
            }
            var newlights = new List<int>();


            for (int i = 0; i < k; i++)//操作する回数
            {
                for (int l = 0; l < n; l++)
                {
                    newlights[l]=0;
                }

                for (int j = 0; j < n; j++)
                {
                    int min = (j + 1) - lights[j];
                    int max = (j + 1) + lights[j];

                    for (int m = 0; m < n; m++)
                    {
                        if (min <= (m + 1) && (m + 1) <= max)
                        {
                            newlights[m]++;
                        }
                    }
                }
                lights = newlights;
            }

            StringBuilder sb = new StringBuilder();
            foreach (int i in lights)
            {
                sb.Append(i.ToString() + " ");
            }
            Console.WriteLine(sb.ToString());

            
        }
    }
}