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

namespace C
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var NK = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var A = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var N = NK[0];
            var K = NK[1];

            var answer = Enumerable.Repeat(N, N).ToArray();
            if (N < K)
            {
                Console.WriteLine(string.Join(" ", answer));
                return;
            }

            answer = A;
            for (var i = 0; i < Math.Min(N, K); i++)
            {
                var isEnd = true;
                var tmp = new int[N];
                for (var j = 0; j < A.Length; j++)
                {
                    tmp[j]++;
                    for (var k = 1; k <= answer[j]; k++)
                    {
                        var left = j - k;
                        var right = j + k;
                        if (left >= 0) tmp[left]++;
                        if (right < N) tmp[right]++;
                    }
                    if (tmp[j] < N) isEnd = false;
                }
                answer = tmp;
                if (isEnd) break;
            }

            Console.WriteLine(string.Join(" ", answer));
        }
    }
}