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.Text;
using System.Collections.Generic;
using System.Collections;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        
        //static long mod = 1000000007;
        //static char[] az = Enumerable.Range('a', 'z' - 'a' + 1).Select(i => (Char)i).ToArray();
        static void Main(string[] args)
        {
            //var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            //var N = long.Parse(Console.ReadLine());
            var NK = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var N = NK[0];
            var K = NK[1];
            var A = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
            
            //var C = new  

            for (int i = 0; i < K && i <= (long)Sqrt(N); i++)
            {
                var B = new int[N];
                for (int j = 0; j < N; j++)
                {
                    B[(int)Max(j - A[j], 0)]++;
                    if (j + A[j] < N - 1) B[(int)Min(j + A[j]+1, N-1)]--;
                }
                for (int j = 1; j < N; j++)
                {
                    B[j] += B[j - 1];
                }
                A = new List<int>(B);
            }
            Console.WriteLine(String.Join(" ",A));
           
        }


    }
}