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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
class c{
  public static void Main(){
    String[] str = Console.ReadLine().Split(' ');
    int n = int.Parse(str[0]);
    int k = int.Parse(str[1]);
    int[] d = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
    for(int i=0; i<k; i++){
      int[] count = new int[n];
      for(int j=1; j<=n; j++){
        int left = (int)Math.Max(1,j-d[j-1]);
        int right = (int)Math.Min(n,j+d[j-1]);
        //Console.WriteLine("{0} {1} {2}",left,right,i);
        for(int x=left; x<=right; x++){
          count[x-1]++;
        }
      }
      for(int j=0; j<n; j++){
        d[j] = count[j];
      }
    }
    Console.WriteLine(string.Join(" ",d));
  }
}