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

namespace debug
{
    class main
    {
        static void Main(string[] args)
        {
            //問題クラスを展開
            ProgramC a = new ProgramC();
            a.main();//実行する

        }

    }

    class ProgramA
    {
        public void main()
        {
            //入力
            string s = Console.ReadLine();

            //時間に換算して起きてる時間からk時間を除く
            Console.WriteLine(s.Substring(0,3));

        }
    }

    class ProgramB
    {
        public void main()
        {
            //入力
            string[] s1 = Console.ReadLine().Split(' ');
            long a = long.Parse(s1[0]);
            long v = long.Parse(s1[1]);
            string[] s2= Console.ReadLine().Split(' ');
            long b = long.Parse(s2[0]);
            long w = long.Parse(s2[1]);
            long t = long.Parse(Console.ReadLine());
            long temp = t * (v - w);

            //?はD、それ以外は普通に出す
            if (temp >= Math.Abs(a - b))
                Console.WriteLine("YES");
            else
                Console.WriteLine("NO");
        }
    }

    class ProgramC
    {
        public void main()
        {
            string[] s = Console.ReadLine().Split(' ');
            long n = long.Parse(s[0]);
            long k = long.Parse(s[1]);
            string[] a1 = Console.ReadLine().Split(' ');

            long[] a = new long[n];

            for (int i = 0; i < n; i++)
                a[i] = long.Parse(a1[i]);


            for (int x = 0; x < k; x++)
            {

                long[] b = new long[n];
                for (int i = 0; i < n; i++)
                {
                    long l = Math.Max(0, i - a[i]);
                    long r = Math.Min(n - 1, i + a[i]);
                    b[l]++;
                    if (r + 1 < n)
                        b[r + 1]--;

                }

                for (int i = 1; i < n; i++)
                    b[i] += b[i - 1];

                for (int i = 0; i < n; i++)
                    a[i] = b[i];

                if (x == 50)
                    break;
            }

            for (int i = 0; i < n; i++)
                Console.Write(a[i] + " ");
        }
    }
}