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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Linq;

class Program
{
    static void Main()
    {
        var NK = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int N = NK[0], K = NK[1];

        var A = Console.ReadLine().Split().Select(int.Parse).ToArray();

        for(int k=0; k<K; ++k) {
            var B = new int[N+1];
            for(int i=0; i<N; ++i) {
                int a = A[i];
                B[Math.Max(0, i-a  )]++;
                B[Math.Min(N, i+a+1)]--;
            }
            int v = 0;
            bool exist_not_N = false;
            for(int i=0; i<N; ++i) {
                v += B[i];
                A[i] = v;
                exist_not_N = exist_not_N || (v!=N);
            }
            if(!exist_not_N) break;
        }

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