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: Accepted)

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

fun main(args: Array<String>) = tokiomarine2020c()

fun tokiomarine2020c() {
    val (n, k) = readLine()!!.split(' ').map { it.toInt() }
    val aList = readLine()!!.split(' ').map { it.toLong() }

    var curr = aList.toLongArray()

    repeat(min(k, 50)) {
        val imos = LongArray(n)

        curr.withIndex().forEach { (index, value) ->
            val left = max(index - value, 0)
            imos[left.toInt()]++

            val right = index + value + 1
            if (right in imos.indices) imos[right.toInt()]--
        }

        for (i in 0 until n - 1) imos[i + 1] += imos[i]

        curr = imos.copyOf()
    }

    val answer = curr.joinToString(" ")

    println(answer)
}