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 Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

import kotlin.math.max
import kotlin.math.min

fun main() {
    val (_, k) = readLine()!!.splitToSequence(" ").map(Integer::parseInt).toList()
    val lamps = readLine()!!.splitToSequence(" ").map(Integer::parseInt).toList()
    val result = (1..k).fold(lamps) { acc, _ ->
        val nextLamps = mutableMapOf<Int, Int>()
        acc.forEachIndexed { x, l ->
            val startX = x - l
            val endX = x + l
            (max(startX, 0)..min(endX, lamps.lastIndex)).forEach {
                val d = nextLamps.getOrDefault(it, 0)
                nextLamps[it] = d + 1
            }
        }
        nextLamps.asSequence()
            .map { it.value }
            .toList()
    }
    println(result.joinToString(" "))
}