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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

const BUFSIZE = 10000000

var rdr = bufio.NewReaderSize(os.Stdin, BUFSIZE)

var ANext [200001]int
var NFlag [200001]bool
var NCount int

func main() {
	var N, K int
	fmt.Scanf("%d %d", &N, &K)
	A := NextLineInt()

	for k := 0; k < K; k++ {
		for i := 0; i < N; i++ {
			ANext[i] = 0
		}

		for x, a := range A {
			ANext[Max(0, x-a)] += 1
			ANext[Min(N, x+a+1)] -= 1
		}

		for i := 0; i < N; i++ {
			ANext[i+1] += ANext[i]
			A[i] = ANext[i]
			if A[i] == N && !NFlag[i] {
				NFlag[i] = true
				NCount += 1
			}
		}

		if NCount == N {
			break
		}
	}

	for _, a := range A {
		fmt.Printf("%d ", a)
	}
}

func NextLineInt() []int {
	buf := make([]byte, 0, BUFSIZE)
	for {
		l, p, e := rdr.ReadLine()
		if e != nil {
			panic(e)
		}

		buf = append(buf, l...)

		if !p {
			break
		}
	}
	str := strings.Split(string(buf), " ")
	l := len(str)

	ret := make([]int, l)

	for i := range str {
		// ret[i], ok = strconv.Atoi(str[i])
		v, ok := strconv.Atoi(str[i])

		if ok == nil {
			ret[i] = int(v)
		}
	}

	return ret
}

func Bool2Int(b bool) int {
	if b {
		return 1
	} else {
		return 0
	}
}

func Abs(v int) int {
	if v < 0 {
		return -v
	}
	return v
}

func Min(a, b int) int {
	if a > b {
		return b
	} else {
		return a
	}
}

func Max(a, b int) int {
	if a > b {
		return a
	} else {
		return b
	}
}

func Distance(a, b int) int {
	return Abs(a - b)
}