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

namespace MyProject
{
    class Program
    {
        static void Main(string[] args)
        {
#if Local
            var sw = new Stopwatch();
            sw.Start();
            Console.SetIn(new StreamReader("input.in"));
#endif

            var solver = new Solver();
            solver.Solve();
#if Local
            Console.WriteLine($"{sw.ElapsedMilliseconds}ms");
#endif
        }
    }

    class Solver
    {
        public List<int> Update(IReadOnlyList<int> A)
        {
            var B = Enumerable.Repeat(0, A.Count).ToList();
            foreach (var i in Enumerable.Range(0, A.Count))
            {
                var l = Math.Max(0, i - A[i]);
                B[l]++;

                var r = Math.Min(A.Count - 1, i + A[i]);
                if (r + 1 < A.Count)
                {
                    B[r + 1]--;
                }
            }

            var sum = 0;
            return Enumerable.Range(0, A.Count).Select(i => sum += B[i]).ToList();
        }

        public void Solve()
        {
            var items = Console.ReadLine().Split().Select(elem => int.Parse(elem)).ToList();
            var N = items[0];
            var K = items[1];
            var A = Console.ReadLine().Split().Select(elem => int.Parse(elem)).ToList();

            foreach (var _ in Enumerable.Range(0, K))
            {
                A = this.Update(A);
                if (A.All(elem => elem == N))
                {
                    break;
                }
            };

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