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

static class Program
{
    static int[] Step(int[] A)
    {
        int N = A.Length;
        var tuples = Enumerable.Range(0, N).Select(i => Tuple.Create(i, 1)).ToList();
        for (int i = 0; i < N; ++i)
        {
            tuples.Add(Tuple.Create(Math.Max(i - A[i], 0), 0));
            tuples.Add(Tuple.Create(Math.Min(i + A[i], N), 2));
        }
        tuples.Sort();

        int cnt = 0;
        var B = new int[N];
        foreach (var t in tuples)
        {
            switch (t.Item2)
            {
            case 0:
                ++cnt;
                break;
            case 1:
                B[t.Item1] = cnt;
                break;
            case 2:
                --cnt;
                break;
            }
        }
        return B;
    }

    static int[] Solve(int N, int K, int[] A)
    {
        for (int i = 0; i < K; ++i)
        {
            A = Step(A);
            if (A.All(a => a == N)) { break; }
        }
        return A;
    }

    static void Main(string[] args)
    {
        var V = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var A = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        Console.WriteLine(string.Join(" ", Solve(V[0], V[1], A)));
    }
}