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)

object Main extends App{
  val sc = new java.util.Scanner(System.in)
  var n = sc.nextDouble()
  var k = sc.nextDouble
  var a = Array.fill(n.asInstanceOf[Int])(sc.nextDouble)
  var b = Array.fill(n.asInstanceOf[Int])(0.0)
  var ka,kb = 0.0
  for (i <- 0 until k.asInstanceOf[Int]){
    for (j <- 1 to n.asInstanceOf[Int]){
      ka = j - a(j-1) - 0.5
      kb = j + a(j-1) + 0.5
      for (kk <- (ka.asInstanceOf[Int] + 1) to kb.asInstanceOf[Int] if kk > 0 & kk <= 5){
        b(kk-1) += 1
      }
    }
    System.arraycopy(b,0,a,0,a.length)
    b = Array.fill(n.asInstanceOf[Int])(0.0)
  }
  for (i <- 0 until n.asInstanceOf[Int]){
    print(a(i).asInstanceOf[Int])
    print(" ")
  }
}