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.*

private fun readLn() = readLine()!! // string line
private fun readInt() = readLn().toInt() // single int
private fun readStrings() = readLn().split(" ") // list of strings
private fun readInts() = readStrings().map { it.toInt() } // list of ints

private fun readLong() = readLn().toLong()
private fun readLongs() = readStrings().map{it.toLong()}

fun main(){
    val (n, k) = readInts()
    val power = readInts()

    val mPower = power.toMutableList()

    for(loop in 1..k){
        val tempPower = mPower.toMutableList() //tempにコピー
        mPower.replaceAll { 0 }
        for(lamp in 1..n){ //各電球に対して
            for(i in 1..n){ //全ての電球と比較
                if(lamp < i){
                    val range = i - tempPower[i-1] - 0.5
                    if(range <= lamp){
                        mPower[lamp -1] += 1
                    }
                }else{
                    val range = i + tempPower[i-1] + 0.5
                    if (range >= lamp){
                        mPower[lamp -1] +=1
                    }
                }
            }
        }
    }


    for(i in 0..(mPower.size -1)){
        print(mPower[i].toString() + " ")
    }

}