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.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;


class Program
{
    static void Main(string[] args)
    {
        // 入力
        //var s = Console.ReadLine();
        //var n = int.Parse(Console.ReadLine());
        int[] nk = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var n = nk[0];
        var k = nk[1];
        int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();

        long[] l = new long[n];
        for (int i = 0; i < n; i++)
        {
            int s = (int)Math.Ceiling(i + 1 - a[i] - 0.5);
            if (s <= 0) s = 1;
            int e = (int)Math.Floor(i + 1 + a[i] + 0.5);
            l[s - 1]++;
            if (e < n) l[e]--;
        }

        for (int i = 1; i < n; i++) l[i] += l[i - 1];

        k = Math.Min(k, 600);
        for (int x = 1; x < k; x++)
        {
            long[] tmp = new long[n];
            Array.Copy(l, tmp, n);
            l = new long[n];
            for (int i = 0; i < n; i++)
            {
                int s = (int)Math.Ceiling(i + 1 - tmp[i] - 0.5);
                if (s <= 0) s = 1;
                int e = (int)Math.Floor(i + 1 + tmp[i] + 0.5);
                l[s - 1]++;
                if (e < n) l[e]--;
            }

            for (int i = 1; i < n; i++) l[i] += l[i - 1];
        }



        // 出力
        for (int i = 0; i < l.Length; i++)
        {
            Console.Write(l[i] + " ");
        }

    }
}