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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

import java.util.Scanner

import scala.collection.mutable
import scala.util.control.Breaks

object Main {

  def main(args: Array[String]): Unit = {
    val sc = new Scanner(System.in)
    //    val n = (Math.pow(10, 5) * 2).toInt
    //    val k = (Math.pow(10, 5) * 2).toInt
    //    var a = mutable.ArrayBuffer.fill(n)(0)
    val n = sc.nextInt()
    val k = sc.nextInt()
    var a = mutable.ArrayBuffer.fill(n)(sc.nextInt())

    val b = new Breaks
    b.breakable {
      (1 to k).foreach { _ =>
        val store = mutable.ArrayBuffer.fill(n)(0)
        (0 until n).foreach { i =>
          val d = a(i)
          (i - d to i + d).foreach { j =>
            if (0 <= j && j <= n - 1) store(j) += 1
          }
        }
        a = store
        if (a.min == n) b.break()
      }
    }
    println(a.mkString(" "))

  }

}