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;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int K = int.Parse(str[1]);
		int[]A = new int[N];
		string[] str2 = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A[i] = int.Parse(str2[i]);
		}
		if(K>=N){
			for(var i=0;i<N;i++){
				A[i] = N;
			}
		} else {
			for(var i=0;i<K;i++){
				var listA = new List<int>();
				var listB = new List<int>();
				for(var j=0;j<N;j++){
					listA.Add(Math.Max(0,j-A[j]));
					listB.Add(A[j]+j+1);
				}
				listA.Sort();
				listB.Sort();
				var a1 = 0;
				var b1 = 0;
				var ct = 0;
				bool flag = true;
				for(var j=0;j<N;j++){
					while(a1<listA.Count && listA[a1]==j){
						ct++;
						a1++;
					}
					while(b1<listB.Count && listB[b1]==j){
						ct--;
						b1++;
					}
					A[j] = ct;
					if(A[j]<N){
						flag = false;
					}
				}
				if(flag){
					break;
				}
			}
		}
		Console.Write(A[0]);
		for(var j=1;j<N;j++){
			Console.Write(" " +A[j]);
        }
	}
}