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.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Numerics;
using System.Runtime.CompilerServices;

namespace AtCoder
{
    class Program
    {

        const int BiggestMod = 1000000007;

        public static void Main()
        {

            var args = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var lumps = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var num = args[0];
            var count = args[1];

            if (count > 50) count = 50;

            for (int i = 0; i < count; i++)
            {
                var memo = new int[num];
                for (int j = 0; j < num; j++)
                    memo[i] = 0;

                for (int j = 0; j < num; j++)
                    for (int k = (j - lumps[j] < 0 ? 0 : j - lumps[j]), end = (j + lumps[j] > num - 1 ? num - 1 : j + lumps[j]);
                        k <= end; k++)
                        memo[k]++;

                lumps = memo;

            }

            Console.WriteLine(string.Join(' ', lumps.ToList().ConvertAll(x => x.ToString())));

        }

    }

}