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"
	"os"
	"strconv"
	"strings"
)

var (
	scanner = bufio.NewScanner(os.Stdin)
	w       = bufio.NewWriter(os.Stdout)
)

func readInt() (read int) {
	scanner.Scan()
	read, err := strconv.Atoi(scanner.Text())
	if err != nil {
		panic(err)
	}
	return
}

func main() {
	scanner.Split(bufio.ScanWords)
	defer w.Flush()

	n := readInt()
	k := readInt()

	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = readInt()
	}

	for i := 0; i < k; i++ {
		next := make([]int, n)
		for j := 0; j < n; j++ {
			for h := 0; h < a[j]+1; h++ {
				if h == 0 {
					next[j]++
				} else {
					if j-h >= 0 {
						next[j-h]++
					}
					if j+h < n {
						next[j+h]++
					}
				}
			}
		}
		a = next
	}

	fmt.Fprintln(w, strings.Trim(fmt.Sprint(a), "[]"))
}