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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
using System.IO;

namespace AtCoder.XXX.C
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var X = cr();
            var n = X[0];
            var k = X[1];
var sb = new StringBuilder();
            var datas = cr();
            var result = new int[n];
            for (var i = 0; i < k; i++)
            {
                for (var j = 1; j < datas.Length + 1; j++)
                {
//P(j+ "-" +datas[j-1] +"- 0.5");
                    var a = j - datas[j-1] - 0.5;
                    var b = j + datas[j-1] + 0.5;
//P("a : "+a+"b : "+b);
                    for (var q = 1; q < datas.Length+1; q++)
                    {
                        if (q> a && q< b)
                        {
//P(q+"を光らせる");
                            result[q-1]++;
                        }
                    }
                }
                datas = new List<int>(result).ToArray();
            }
sb = new StringBuilder();
            foreach(var a in result)
			{
               sb.Append(a +" ");
			}
P(sb.ToString());


        }

        private static StreamReader sr;
        public static int[] Ecr()
        {
            if (sr == null)
            {
                sr = new StreamReader("input.txt", Encoding.GetEncoding("UTF-8"));
            }
            return sr.ReadLine().Split().Select(int.Parse).ToArray();
        }
        public static int[] cr()
        {
            return Console.ReadLine().Split().Select(int.Parse).ToArray();
        }
        public static string Er()
        {
            if (sr == null)
            {
                sr = new StreamReader("input.txt", Encoding.GetEncoding("UTF-8"));
            }
            return sr.ReadLine();
        }
        public static string r()
        {
            return Console.ReadLine();
        }
        public static int cri()
        {
            return int.Parse(Console.ReadLine());
        }
        public static void P(string str)
        {
            Console.WriteLine(str);
        }
        public static void P(int num)
        {
            P(num.ToString());
        }
    }
}