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: Wrong Answer)

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

class Program {
    static void Main (string[] args) {
        var input = INP();
        var input2 = INP();

        int N = TOI(input[0]);
        int K = TOI(input[1]);
        long[] A = new long[N];
        for(int i = 0;i < N;i++) {
            A[i] = TOL(input2[i]);
        }

        for(int j = 0;j < K;j++) {
            A[j] += checks(N,A);
        }

        for(int i = 0;i < N;i++) {
            Console.Write(A[i]);
            Console.Write(" ");
        }
    }

    static long checks (long num,long[] nums) {
        long result = 0;
        for(int i = 0;i < num;i++) {
            result += Math.Abs(nums[i] - i) >= 1 ? nums[i] : 0;
        }

        return result;
    }

    static string[] INP () {
        return Console.ReadLine().Split(' ');
    }

    static void CWL (string value) {
        Console.WriteLine(value);
    }

    static void CWL (int value) {
        Console.WriteLine(value);
    }

    static void CWL (long value) {
        Console.WriteLine(value);
    }

    static void CWL (float value) {
        Console.WriteLine(value);
    }

    static void CWL (double value) {
        Console.WriteLine(value);
    }

    static int TOI (string str) {
        return int.Parse(str);
    }

    static long TOL (string str) {
        return long.Parse(str);
    }

    static float TOF (string str) {
        return float.Parse(str);
    }

    static double TOD (string str) {
        return double.Parse(str);
    }

    /*static void Main (string[] args) {
        var input = INP();
        var input2 = INP();
        var input3 = INP();

        CWL("dummy");
    }*/
}