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: Time Limit Exceeded)

package main

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

func main() {
	n := readInt64()
	k := int(readInt64())
	a := readInt64Slice(n)

	ans := map[int]map[int]bool{}

	for i := 0; i < int(n); i++ {
		ans[i] = map[int]bool{i: true}
	}

	for i := 0; i < k; i++ {
		for j, v := range a {
			for l := j - int(v); l <= j+int(v); l++ {
				if l < 0 {
					continue
				}
				if l >= int(n) {
					continue
				}
				if l == j {
					continue
				}
				ans[l][j] = true
			}
		}

		for j := range a {
			a[j] = int64(len(ans[j]))
		}

	}

	for _, v := range a {
		fmt.Print(v, " ")
	}
	fmt.Println()

}

var (
	scanner *bufio.Scanner
)

func init() {
	scanner = bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
}

func readInt64() int64 {
	var t string

	if scanner.Scan() {
		t = scanner.Text()
	}

	n, err := strconv.ParseInt(t, 10, 64)
	if err != nil {
		log.Fatal(err)
	}

	return n

}

func readInt64Slice(n int64) []int64 {
	s := make([]int64, n)
	var t string

	for i := 0; i < int(n); i++ {
		if scanner.Scan() {
			t = scanner.Text()
		}

		num, err := strconv.ParseInt(t, 10, 64)
		if err != nil {
			log.Fatal(err)
		}
		s[i] = num
	}

	return s
}